Bulletin of the London Mathematical Society最新文献

{"title":"Holonomy of the Obata connection on 2-step hypercomplex nilmanifolds","authors":"Adrián Andrada,&nbsp;María Laura Barberis,&nbsp;Beatrice Brienza","doi":"10.1112/blms.70338","DOIUrl":"https://doi.org/10.1112/blms.70338","url":null,"abstract":"<p>We study the holonomy of the Obata connection on 2-step hypercomplex nilmanifolds. By explicitly computing the curvature tensor, we determine the conditions under which the Obata connection is flat, showing that this depends on the nilpotency step of each complex structure. In particular, we show that for 2-step hypercomplex nilmanifolds, the holonomy algebra of the Obata connection is always an abelian subalgebra of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>sl</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>,</mo>\u0000 <mi>H</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathfrak {sl}(n, mathbb {H})$</annotation>\u0000 </semantics></math> and we prove that the <span></span><math>\u0000 <semantics>\u0000 <mi>H</mi>\u0000 <annotation>$mathbb {H}$</annotation>\u0000 </semantics></math>-solvable conjecture holds in this case. Furthermore, we provide new examples of <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math>-step nilpotent hypercomplex nilmanifolds, with arbitrary <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math>, which are not Obata flat.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147569058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"O-minimal total harmonic functions are polynomial","authors":"Chris Miller","doi":"10.1112/blms.70278","DOIUrl":"https://doi.org/10.1112/blms.70278","url":null,"abstract":"<p>If <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>h</mi>\u0000 <mo>:</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mo>→</mo>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <annotation>$hcolon mathbb {R}^n rightarrow mathbb {R}$</annotation>\u0000 </semantics></math> is harmonic and definable in an o-minimal expansion of the real field, then <span></span><math>\u0000 <semantics>\u0000 <mi>h</mi>\u0000 <annotation>$h$</annotation>\u0000 </semantics></math> is polynomial.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147568270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quasibounded solutions to the complex Monge–Ampère equation","authors":"Mårten Nilsson","doi":"10.1112/blms.70340","DOIUrl":"https://doi.org/10.1112/blms.70340","url":null,"abstract":"<p>We study the Dirichlet problem for the complex Monge–Ampère operator on B-regular domains in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$mathbb {C}^n$</annotation>\u0000 </semantics></math>, allowing boundary data that is singular or unbounded. We extend the concept of pluri-quasibounded functions on the domain to functions on the boundary, defined by the existence of plurisuperharmonic majorants that dominate their absolute value in a strong sense—that is, the ratio of the function to the majorant tends to zero as the function tends to infinity. For such boundary data, we prove existence and uniqueness of pluri-quasibounded solutions in the Błocki–Cegrell class, the largest class for which the complex Monge–Ampère operator is well-behaved. In the unit disk, our approach recovers harmonic functions represented as Poisson integrals of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$L^1$</annotation>\u0000 </semantics></math> boundary data with respect to harmonic measure, and our characterization extends to all regular domains in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$mathbb {R}^n$</annotation>\u0000 </semantics></math>, when the boundary data is continuous almost everywhere. We also describe how boundary singularities propagate into the interior via a refined pluripolar hull.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70340","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147567943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A computer-free property (T) proof for high-rank \u0000 \u0000 \u0000 Aut\u0000 (\u0000 \u0000 F\u0000 n\u0000 \u0000 )\u0000 \u0000 $mathrm{Aut}(F_n)$","authors":"Martin Nitsche","doi":"10.1112/blms.70334","DOIUrl":"https://doi.org/10.1112/blms.70334","url":null,"abstract":"<p>Existing property (T) proofs for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Aut</mi>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{Aut}(F_n)$</annotation>\u0000 </semantics></math>, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>⩾</mo>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 <annotation>$ngeqslant 4$</annotation>\u0000 </semantics></math>, rely crucially on extensive computer calculations. We give a new proof that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Aut</mi>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{Aut}(F_n)$</annotation>\u0000 </semantics></math> has property (T) for all but finitely many <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>, which is inspired by the semidefinite programming approach but does not use the computer in any step. More specifically, we prove property (T) for a certain extension <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>Γ</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <annotation>$Gamma _n$</annotation>\u0000 </semantics></math> of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>SAut</mi>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{SAut}(F_n)$</annotation>\u0000 </semantics></math> as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>→</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$nrightarrow infty$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147567410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Chromatic number and regular subgraphs","authors":"Barnabás Janzer,&nbsp;Raphael Steiner,&nbsp;Benny Sudakov","doi":"10.1112/blms.70262","DOIUrl":"https://doi.org/10.1112/blms.70262","url":null,"abstract":"&lt;p&gt;In 1992, Erdős and Hajnal posed the following natural problem: Does there exist, for every &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$rin mathbb {N}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, an integer &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$F(r)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; such that every graph with chromatic number at least &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$F(r)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; contains &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;annotation&gt;$r$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; edge-disjoint cycles on the same vertex set? We solve this problem in a strong form, by showing that there exist &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;annotation&gt;$n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-vertex graphs with fractional chromatic number &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;log&lt;/mi&gt;\u0000 &lt;mi&gt;log&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;log&lt;/mi&gt;\u0000 &lt;mi&gt;log&lt;/mi&gt;\u0000 &lt;mi&gt;log&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Omega left(frac{log log n}{log log log n}right)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; that do not even contain a 4-regular subgraph. This implies that no such number &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$F(r)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; exists for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;⩾&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotatio","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70262","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Symmetrization and the rate of convergence of semigroups of holomorphic functions","authors":"Dimitrios Betsakos,&nbsp;Argyrios Christodoulou","doi":"10.1112/blms.70337","DOIUrl":"https://doi.org/10.1112/blms.70337","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ϕ&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(phi _t)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;⩾&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$tgeqslant 0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, be a semigroup of holomorphic self-maps of the unit disk &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathbb {D}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;annotation&gt;$Omega$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be its Koenigs domain and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;τ&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$tau in partial mathbb {D}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be its Denjoy–Wolff point. Suppose that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$0in Omega$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;♯&lt;/mo&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$Omega ^sharp$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be the Steiner symmetrization of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;annotation&gt;$Omega$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with respect to the real axis. Consider the semigroup &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;ϕ&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;♯&lt;/mo&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(phi _t^sharp)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with Koenigs domain &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;♯&lt;/mo&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$Omega ^sharp$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 ","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70337","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Ruzsa's conjecture on congruence preserving functions","authors":"É. Delaygue","doi":"10.1112/blms.70332","DOIUrl":"https://doi.org/10.1112/blms.70332","url":null,"abstract":"&lt;p&gt;Ruzsa's conjecture asserts that any sequence &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;⩾&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;${(a_n)}_{n geqslant 0}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of integers that preserves congruences, that is, satisfies &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;≡&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mi&gt;mod&lt;/mi&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$ a_{n+k} equiv a_n mod {k}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, and has the growth condition &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mo&gt;lim sup&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$limsup _{n rightarrow +infty } |a_n|^{1/n} &lt; e$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, must be a polynomial sequence. While previous results by Hall, Ruzsa, Perelli, and Zannier have confirmed this conjecture under stricter growth bounds, the general case remains open. In this paper, we establish a new partial result by proving that if in addition the generating series &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mo&gt;∑&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 ","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the uniform flatness of polynomial graphs","authors":"Xieping Wang,&nbsp;Li Zhang","doi":"10.1112/blms.70253","DOIUrl":"https://doi.org/10.1112/blms.70253","url":null,"abstract":"<p>This paper grew out of an effort to understand the so-called uniform flatness, an important concept in the Bargmann–Fock interpolation theory developed by Varolin et al. We show that the graph of every polynomial in one complex variable is a uniformly flat algebraic curve in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$mathbb {C}^2$</annotation>\u0000 </semantics></math>, with vanishing upper density with respect to the Gaussian weight. Combined with a result of Pingali and Varolin, this implies that such graphs are interpolating for the Bargmann–Fock space on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$mathbb {C}^2$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Revisiting \u0000 \u0000 \u0000 (\u0000 ∞\u0000 ,\u0000 2\u0000 )\u0000 \u0000 ${(infty,2)}$\u0000 -naturality of the Yoneda embedding","authors":"Tobias Lenz","doi":"10.1112/blms.70254","DOIUrl":"https://doi.org/10.1112/blms.70254","url":null,"abstract":"<p>We show that the Yoneda embedding ‘is’ <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>∞</mi>\u0000 <mo>,</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(infty,2)$</annotation>\u0000 </semantics></math>-natural with respect to the functoriality of presheaves via left Kan extension, refining the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>∞</mi>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(infty,1)$</annotation>\u0000 </semantics></math>-categorical result proven independently by Haugseng–Hebestreit–Linskens–Nuiten and Ramzi, and answering a question of Ben-Moshe.</p><p>As the key technical ingredient, we show that the identity functor of the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>∞</mi>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(infty,1)$</annotation>\u0000 </semantics></math>-category of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>∞</mi>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(infty,1)$</annotation>\u0000 </semantics></math>-categories admits only one enhancement to an <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>∞</mi>\u0000 <mo>,</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(infty,2)$</annotation>\u0000 </semantics></math>-functor (namely, the identity functor).</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 4","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70254","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Reciprocity for \u0000 \u0000 \u0000 G\u0000 L\u0000 (\u0000 2\u0000 )\u0000 \u0000 $GL(2)$\u0000 \u0000 \u0000 L\u0000 $L$\u0000 -functions twisted by Dirichlet characters","authors":"Agniva Dasgupta,&nbsp;Rizwanur Khan,&nbsp;Ze Sen Tang","doi":"10.1112/blms.70316","DOIUrl":"https://doi.org/10.1112/blms.70316","url":null,"abstract":"<p>A formula connecting a moment of <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math>-functions and a dual moment in a way that interchanges the roles of certain key parameters on both sides is known as a reciprocity relation. We establish a reciprocity relation for a first moment of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 <mi>L</mi>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$GL(2)$</annotation>\u0000 </semantics></math> <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math>-functions twisted by Dirichlet characters. This extends, via a new and simple argument, some results of Bettin, Drappeau, and Nordentoft.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 3","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147562892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}