Journal of the London Mathematical Society-Second Series最新文献

{"title":"Jacobi forms of weight 1 on \u0000 \u0000 \u0000 \u0000 Γ\u0000 0\u0000 \u0000 \u0000 (\u0000 N\u0000 )\u0000 \u0000 \u0000 $mathbf {Gamma _0(N)}$","authors":"Jialin Li, Haowu Wang","doi":"10.1112/jlms.70306","DOIUrl":"https://doi.org/10.1112/jlms.70306","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>J</mi>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>N</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$J_{1,m}(N)$</annotation>\u0000 </semantics></math> be the vector space of Jacobi forms of weight one and index <span></span><math>\u0000 <semantics>\u0000 <mi>m</mi>\u0000 <annotation>$m$</annotation>\u0000 </semantics></math> on <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>Γ</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>N</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$Gamma _0(N)$</annotation>\u0000 </semantics></math>. In 1985, Skoruppa proved that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>J</mi>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$J_{1,m}(1)=0$</annotation>\u0000 </semantics></math> for all <span></span><math>\u0000 <semantics>\u0000 <mi>m</mi>\u0000 <annotation>$m$</annotation>\u0000 </semantics></math>. In 2007, Ibukiyama and Skoruppa proved that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>J</mi>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>N</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$J_{1,m}(N)=0$</annotation>\u0000 </semantics></math> for all <span></span><math>\u0000 <semantics>\u0000 <mi>m</mi>\u0000 <annotation>$m$</annotation>\u0000 </semantics></math> and all squarefree <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$N$</annotation>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145181519","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the equality of three formulas for Brumer–Stark units","authors":"Samit Dasgupta,&nbsp;Matthew H. L. Honnor,&nbsp;Michael Spieß","doi":"10.1112/jlms.70296","DOIUrl":"https://doi.org/10.1112/jlms.70296","url":null,"abstract":"<p>We prove the equality of three conjectural formulas for Brumer–Stark units. The first formula has essentially been proven, so this paper also verifies the validity of the other two formulas.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145224422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dirac–Schrödinger operators, index theory and spectral flow","authors":"Koen van den Dungen","doi":"10.1112/jlms.70301","DOIUrl":"https://doi.org/10.1112/jlms.70301","url":null,"abstract":"<p>In this article, we study generalised Dirac–Schrödinger operators in arbitrary signatures (with or without gradings), providing a general <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>K</mi>\u0000 <mi>K</mi>\u0000 </mrow>\u0000 <annotation>$textnormal {KK}$</annotation>\u0000 </semantics></math>-theoretic framework for the study of index pairings and spectral flow. We provide a general Callias Theorem, which shows that the index (or the spectral flow, or abstractly the <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$textnormal {K}$</annotation>\u0000 </semantics></math>-theory class) of Dirac–Schrödinger operators can be computed on a suitable compact hypersurface. Furthermore, if the zero eigenvalue is isolated in the spectrum of the Dirac operator, we relate the index (or spectral flow) of Dirac–Schrödinger operators to the index (or spectral flow) of corresponding Toeplitz operators. Combining both results, we obtain an index (or spectral flow) equality relating Toeplitz operators on the non-compact manifold to Toeplitz operators on the compact hypersurface. Our results generalise various known results from the literature, while presenting these results in a common unified framework.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70301","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145181617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"De Rham \u0000 \u0000 F\u0000 $F$\u0000 -gauges and Shimura varieties","authors":"Xu Shen","doi":"10.1112/jlms.70309","DOIUrl":"https://doi.org/10.1112/jlms.70309","url":null,"abstract":"<p>We study <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-gauges for de Rham cohomology of smooth algebraic varieties in characteristic <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>. Applying to good reductions of Shimura varieties of Hodge type, we recover the Ekedahl–Oort stratifications by constructing universal de Rham <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-gauges with <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>-structure. We also study the cohomology of de Rham <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-gauges on these varieties. In particular, in the PEL-type case and when the weights of the flat automorphic vector bundles are <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-small, we determine the <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-gauge structure on their de Rham cohomology by the associated dual Bernstein-Gelfand-Gelfand (BGG) complexes.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145224360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Jucys–Murphy method and fusion procedure for the Sergeev superalgebra","authors":"Iryna Kashuba,&nbsp;Alexander Molev,&nbsp;Vera Serganova","doi":"10.1112/jlms.70302","DOIUrl":"10.1112/jlms.70302","url":null,"abstract":"<p>We use the Jucys–Murphy elements to construct a complete set of primitive idempotents for the Sergeev superalgebra <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>S</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <annotation>${mathcal {S}}_n$</annotation>\u0000 </semantics></math>. We produce seminormal forms for the simple modules over <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>S</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <annotation>${mathcal {S}}_n$</annotation>\u0000 </semantics></math> and over the spin symmetric group algebra with explicit constructions of basis vectors. We show that the idempotents can also be obtained from a new version of the fusion procedure.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70302","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145111282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Density cardinals","authors":"Christina Brech,&nbsp;Jörg Brendle,&nbsp;Márcio Telles","doi":"10.1112/jlms.70300","DOIUrl":"10.1112/jlms.70300","url":null,"abstract":"<p>How many permutations are needed so that every infinite–coinfinite set of natural numbers with asymptotic density can be rearranged to no longer have the same density? We prove that the density number <span></span><math>\u0000 <semantics>\u0000 <mi>dd</mi>\u0000 <annotation>${mathfrak {dd}}$</annotation>\u0000 </semantics></math>, which answers this question, is equal to the least size of a nonmeager set of reals, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>non</mi>\u0000 <mo>(</mo>\u0000 <mi>M</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>${mathsf {non}}({mathcal {M}})$</annotation>\u0000 </semantics></math>. The same argument shows that a slight modification of the rearrangement number <span></span><math>\u0000 <semantics>\u0000 <mi>rr</mi>\u0000 <annotation>${mathfrak {rr}}$</annotation>\u0000 </semantics></math> of Blass et al. [Trans. Amer. Math. Soc. <b>373</b> (2020), no. 1, 41–69]is equal to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>non</mi>\u0000 <mo>(</mo>\u0000 <mi>M</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>${mathsf {non}}({mathcal {M}})$</annotation>\u0000 </semantics></math>, and similarly for a cardinal invariant related to large-scale topology introduced by Banakh [3], thus answering a question of the latter. We then consider variants of <span></span><math>\u0000 <semantics>\u0000 <mi>dd</mi>\u0000 <annotation>${mathfrak {dd}}$</annotation>\u0000 </semantics></math> given by restricting the possible densities of the original set and/or of the permuted set, providing lower and upper bounds for these cardinals and proving consistency of strict inequalities. We finally look at cardinals defined in terms of relative density and of asymptotic mean, and relate them to the rearrangement numbers of Blass et al. [Trans. Amer. Math. Soc. <b>373</b> (2020), no. 1, 41–69].</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70300","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145101447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stochastic integration with respect to cylindrical Lévy processes in Hilbert spaces","authors":"Gergely Bodó,&nbsp;Markus Riedle","doi":"10.1112/jlms.70298","DOIUrl":"10.1112/jlms.70298","url":null,"abstract":"<p>In this work, we present a comprehensive theory of stochastic integration with respect to arbitrary cylindrical Lévy processes in Hilbert spaces. As cylindrical Lévy processes do not enjoy a semimartingale decomposition, our approach relies on an alternative approach to stochastic integration by decoupled tangent sequences. The space of deterministic integrands is identified as a modular space described in terms of the characteristics of the cylindrical Lévy process. The space of random integrands is described as the space of predictable processes whose trajectories are in the space of deterministic integrands almost surely. The derived space of random integrands is verified as the largest space of potential integrands, based on a classical definition of stochastic integrability. We apply the introduced theory of stochastic integration to establish a dominated convergence theorem.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70298","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145101692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Free energy of spherical Coulomb gases with point charges","authors":"Sung-Soo Byun,&nbsp;Nam-Gyu Kang,&nbsp;Seong-Mi Seo,&nbsp;Meng Yang","doi":"10.1112/jlms.70294","DOIUrl":"10.1112/jlms.70294","url":null,"abstract":"<p>We consider two-dimensional Coulomb gases on the Riemann sphere with determinantal or Pfaffian structures, under external potentials that are invariant under rotations around the axis connecting the north and south poles, and with microscopic point charges inserted at the poles. These models can be interpreted as Coulomb gases on the complex plane with weakly confining potentials, where the associated droplet is the entire complex plane. For these models, we derive precise asymptotic expansions of the free energies, including the constant terms.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70294","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145101448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Large deviations for the log-Gamma polymer","authors":"Tom Claeys,&nbsp;Julian Mauersberger","doi":"10.1112/jlms.70295","DOIUrl":"10.1112/jlms.70295","url":null,"abstract":"<p>We conjecture an explicit expression for the lower tail large deviation rate function of the partition function of the log-Gamma polymer. We rigorously prove our result, except for one step for which we only provide heuristic evidence. We show that the large deviation rate function matches with that of last passage percolation with exponential weights in the zero-temperature limit, and with the lower tail of the Tracy–Widom distribution for moderate deviations.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145101449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On multiplicative recurrence along linear patterns","authors":"Dimitrios Charamaras,&nbsp;Andreas Mountakis,&nbsp;Konstantinos Tsinas","doi":"10.1112/jlms.70292","DOIUrl":"10.1112/jlms.70292","url":null,"abstract":"&lt;p&gt;Donoso, Le, Moreira, and Sun (&lt;i&gt;J. Anal. Math&lt;/i&gt;. 149 (2023), 719–761) study sets of recurrence for actions of the multiplicative 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;mi&gt;N&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mo&gt;×&lt;/mo&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(mathbb {N}, times)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and provide some sufficient conditions for sets of the form &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;b&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;c&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$S=lbrace (an+b)/(cn+d) colon n in mathbb {N}rbrace $&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; to be sets of recurrence for such actions. A necessary condition for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;annotation&gt;$S$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; to be a set of multiplicative recurrence is that for every completely multiplicative function &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;annotation&gt;$f$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; taking values on the unit circle, we have that &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 inf&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&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;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;b&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;c&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70292","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145101334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}