Josep Fontana-McNally , Eva Miranda , Cédric Oms , Daniel Peralta-Salas
{"title":"A counterexample to the singular Weinstein conjecture","authors":"Josep Fontana-McNally , Eva Miranda , Cédric Oms , Daniel Peralta-Salas","doi":"10.1016/j.aim.2024.109998","DOIUrl":"10.1016/j.aim.2024.109998","url":null,"abstract":"<div><div>In this article, we study the dynamical properties of Reeb vector fields on <em>b</em>-contact manifolds. We show that in dimension 3, the number of so-called singular periodic orbits can be prescribed. These constructions illuminate some key properties of escape orbits and singular periodic orbits, which play a central role in formulating singular counterparts to the Weinstein conjecture and the Hamiltonian Seifert conjecture. In fact, we prove that the above-mentioned constructions lead to counterexamples of these conjectures as stated in <span><span>[20]</span></span>. Our construction shows that there are <em>b</em>-contact manifolds with no singular periodic orbits and no regular periodic orbits away from <em>Z</em>. We do not know whether there are constructions with no generalized escape orbits whose <em>α and ω</em>-limits both lie on <em>Z</em> (a generalized singular periodic orbit). This is the content of the <em>generalized Weinstein conjecture</em>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Steiner inequality for the Lp surface area","authors":"Zixin Cao , Tuo Wang , Yanhui Wang","doi":"10.1016/j.aim.2024.109997","DOIUrl":"10.1016/j.aim.2024.109997","url":null,"abstract":"<div><div>The Steiner inequalities for the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> surface area are established for <span><math><mi>p</mi><mo>></mo><mn>1</mn></math></span>. As a consequence, we give a new proof of Lutwak's <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> isoperimetric inequalities for <span><math><mi>p</mi><mo>></mo><mn>1</mn></math></span> together with their equality conditions.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142560997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Conformal measure rigidity for representations via self-joinings","authors":"Dongryul M. Kim, Hee Oh","doi":"10.1016/j.aim.2024.109992","DOIUrl":"10.1016/j.aim.2024.109992","url":null,"abstract":"<div><div>Let Γ be a Zariski dense discrete subgroup of a connected simple real algebraic group <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>. We discuss a rigidity problem for discrete faithful representations <span><math><mi>ρ</mi><mo>:</mo><mi>Γ</mi><mo>→</mo><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> and a surprising role played by higher rank conformal measures of the associated self-joining group. Our approach recovers rigidity theorems of Sullivan, Tukia and Yue, as well as applies to Anosov representations, including Hitchin representations.</div><div>More precisely, for a given representation <em>ρ</em> with a boundary map <em>f</em> defined on the limit set Λ, we ask whether the extendability of <em>ρ</em> to <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> can be detected by the property that <em>f</em> pushes forward some Γ-conformal measure class <span><math><mo>[</mo><msub><mrow><mi>ν</mi></mrow><mrow><mi>Γ</mi></mrow></msub><mo>]</mo></math></span> to a <span><math><mi>ρ</mi><mo>(</mo><mi>Γ</mi><mo>)</mo></math></span>-conformal measure class <span><math><mo>[</mo><msub><mrow><mi>ν</mi></mrow><mrow><mi>ρ</mi><mo>(</mo><mi>Γ</mi><mo>)</mo></mrow></msub><mo>]</mo></math></span>. When Γ is of divergence type in a rank one group or when <em>ρ</em> arises from an Anosov representation, we give an affirmative answer by showing that if the self-joining <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>ρ</mi></mrow></msub><mo>=</mo><mo>(</mo><mtext>id</mtext><mo>×</mo><mi>ρ</mi><mo>)</mo><mo>(</mo><mi>Γ</mi><mo>)</mo></math></span> is Zariski dense in <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>×</mo><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, then the push-forward measures <span><math><msub><mrow><mo>(</mo><mtext>id</mtext><mo>×</mo><mi>f</mi><mo>)</mo></mrow><mrow><mo>⁎</mo></mrow></msub><msub><mrow><mi>ν</mi></mrow><mrow><mi>Γ</mi></mrow></msub></math></span> and <span><math><msub><mrow><mo>(</mo><msup><mrow><mi>f</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>×</mo><mtext>id</mtext><mo>)</mo></mrow><mrow><mo>⁎</mo></mrow></msub><msub><mrow><mi>ν</mi></mrow><mrow><mi>ρ</mi><mo>(</mo><mi>Γ</mi><mo>)</mo></mrow></msub></math></span>, which are higher rank <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>ρ</mi></mrow></msub></math></span>-conformal measures, cannot be in the same measure class.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142560996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Irregular sampling for hyperbolic secant type functions","authors":"Anton Baranov , Yurii Belov","doi":"10.1016/j.aim.2024.109981","DOIUrl":"10.1016/j.aim.2024.109981","url":null,"abstract":"<div><div>We study Gabor frames in the case when the window function is of hyperbolic secant type, i.e., <span><math><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msup><mrow><mo>(</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>a</mi><mi>x</mi></mrow></msup><mo>+</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>b</mi><mi>x</mi></mrow></msup><mo>)</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span>, <span><math><mrow><mi>Re</mi></mrow><mspace></mspace><mi>a</mi><mo>,</mo><mrow><mi>Re</mi></mrow><mspace></mspace><mi>b</mi><mo>></mo><mn>0</mn></math></span>. A criterion for half-regular sampling is obtained: for a separated <span><math><mi>Λ</mi><mo>⊂</mo><mi>R</mi></math></span> the Gabor system <span><math><mi>G</mi><mo>(</mo><mi>g</mi><mo>,</mo><mi>Λ</mi><mo>×</mo><mi>α</mi><mi>Z</mi><mo>)</mo></math></span> is a frame in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo></math></span> if and only if <span><math><msup><mrow><mi>D</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>(</mo><mi>Λ</mi><mo>)</mo><mo>></mo><mi>α</mi></math></span> where <span><math><msup><mrow><mi>D</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>(</mo><mi>Λ</mi><mo>)</mo></math></span> is the usual (Beurling) lower density of Λ. This extends a result by Gröchenig, Romero, and Stöckler which applies to the case of a standard hyperbolic secant. Also, a full description of complete interpolating sequences for the shift-invariant space generated by <em>g</em> is given.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Curvature operators and rational cobordism","authors":"Renato G. Bettiol , McFeely Jackson Goodman","doi":"10.1016/j.aim.2024.109995","DOIUrl":"10.1016/j.aim.2024.109995","url":null,"abstract":"<div><div>We determine linear inequalities on the eigenvalues of curvature operators that imply vanishing of the twisted <span><math><mover><mrow><mi>A</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> genus on a closed Riemannian spin manifold, where the twisting bundle is any prescribed parallel bundle of tensors. These inequalities yield surgery-stable curvature conditions tailored to annihilate further rational cobordism invariants, such as the Witten genus, elliptic genus, signature, and even the rational cobordism class itself.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Prandtl-Batchelor flows on an annulus","authors":"Mingwen Fei , Chen Gao , Zhiwu Lin , Tao Tao","doi":"10.1016/j.aim.2024.109994","DOIUrl":"10.1016/j.aim.2024.109994","url":null,"abstract":"<div><div>For steady two-dimensional Navier-Stokes flows with a single eddy (i.e. nested closed streamlines) in a simply connected domain, Prandtl (1905) and Batchelor (1956) found that in the inviscid limit, the vorticity is constant inside the eddy. In this paper, we consider the generalized Prandtl-Batchelor theory for the forced steady Navier-Stokes equations on an annulus. First, we observe that in the limit of infinite Reynolds number, if the streamlines of forced steady Navier-Stokes solutions on an annulus are nested closed, then the inviscid limit is a rotating shear flow uniquely determined by the external force and boundary conditions. We call solutions of steady Navier-Stokes equations with the above property Prandtl-Batchelor flows. Then, by constructing higher order approximate solutions of the forced steady Navier-Stokes equations and establishing the validity of Prandtl boundary layer expansion, we give a rigorous proof of the existence of Prandtl-Batchelor flows on an annulus with the wall velocities slightly different from the rigid-rotations along the same direction.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The inequalities of Chern classes and Riemann-Roch type inequalities","authors":"Xing Lu, Jian Xiao","doi":"10.1016/j.aim.2024.109982","DOIUrl":"10.1016/j.aim.2024.109982","url":null,"abstract":"<div><div>Motivated by Kollár-Matsusaka's Riemann-Roch type inequalities, applying effective very ampleness of adjoint bundles on Fujita conjecture and log-concavity given by Khovanskii-Teissier inequalities, we show that for any partition <em>λ</em> of the positive integer <em>d</em> there exists a universal bivariate polynomial <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math></span> which has <span><math><mi>deg</mi><mo></mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>≤</mo><mi>d</mi></math></span> and whose coefficients depend only on <em>n</em> and <em>λ</em>, such that for any projective manifold <em>X</em> of dimension <em>n</em> and any ample line bundle <em>L</em> on <em>X</em>,<span><span><span><math><mrow><mo>|</mo><msub><mrow><mi>c</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo><mo>⋅</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>n</mi><mo>−</mo><mi>d</mi></mrow></msup><mo>|</mo></mrow><mo>≤</mo><mfrac><mrow><msub><mrow><mi>Q</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>,</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>⋅</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow><mrow><msup><mrow><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></mfrac><mo>,</mo></math></span></span></span> where <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> is the canonical bundle of <em>X</em> and <span><math><msub><mrow><mi>c</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is the monomial Chern class given by the partition <em>λ</em>. As a special case, when <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> or <span><math><mo>−</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> is ample, this implies that there exists a constant <span><math><msub><mrow><mi>c</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> depending only on <em>n</em> such that for any monomial Chern classes of top degree, the Chern number ratios satisfy the following inequality<span><span><span><math><mrow><mo>|</mo><mfrac><mrow><msub><mrow><mi>c</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mrow><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub><msup><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup></mrow></mfrac><mo>|</mo></mrow><mo>≤</mo><msub><mrow><mi>c</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo></math></span></span></span> which recovers a recent result of Du-Sun. The main result also yields an asymptotic version of the sharper Riemann-Roch type inequality. Furthermore, using similar method we also obtain inequalities for","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Brown-Peterson spectrum is not E2(p2+2) at odd primes","authors":"Andrew Senger","doi":"10.1016/j.aim.2024.109996","DOIUrl":"10.1016/j.aim.2024.109996","url":null,"abstract":"<div><div>We show that the odd-primary Brown-Peterson spectrum BP does not admit the structure of an <span><math><msub><mrow><mi>E</mi></mrow><mrow><mn>2</mn><mo>(</mo><msup><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>2</mn><mo>)</mo></mrow></msub></math></span> ring spectrum and that there can be no map <span><math><mrow><mi>MU</mi></mrow><mo>→</mo><mrow><mi>BP</mi></mrow></math></span> of <span><math><msub><mrow><mi>E</mi></mrow><mrow><mn>2</mn><mi>p</mi><mo>+</mo><mn>3</mn></mrow></msub></math></span> ring spectra. We also prove the same results for truncated Brown-Peterson spectra <span><math><mrow><mi>BP</mi></mrow><mo>〈</mo><mi>n</mi><mo>〉</mo></math></span> of height <span><math><mi>n</mi><mo>≥</mo><mn>4</mn></math></span>. This extends results of Lawson at the prime 2.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Stefan Glock , David Munhá Correia , Benny Sudakov
{"title":"Hamilton cycles in pseudorandom graphs","authors":"Stefan Glock , David Munhá Correia , Benny Sudakov","doi":"10.1016/j.aim.2024.109984","DOIUrl":"10.1016/j.aim.2024.109984","url":null,"abstract":"<div><div>Finding general conditions which ensure that a graph is Hamiltonian is a central topic in graph theory. An old and well-known conjecture in the area states that any <em>d</em>-regular <em>n</em>-vertex graph <em>G</em> whose second largest eigenvalue in absolute value <span><math><mi>λ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is at most <span><math><mi>d</mi><mo>/</mo><mi>C</mi></math></span>, for some universal constant <span><math><mi>C</mi><mo>></mo><mn>0</mn></math></span>, has a Hamilton cycle. In this paper, we obtain two main results which make substantial progress towards this problem. Firstly, we settle this conjecture in full when the degree <em>d</em> is at least a small power of <em>n</em>. Secondly, in the general case we show that <span><math><mi>λ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≤</mo><mi>d</mi><mo>/</mo><mi>C</mi><msup><mrow><mo>(</mo><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></mrow><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup></math></span> implies the existence of a Hamilton cycle, improving the 20-year old bound of <span><math><mi>d</mi><mo>/</mo><msup><mrow><mi>log</mi></mrow><mrow><mn>1</mn><mo>−</mo><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msup><mo></mo><mi>n</mi></math></span> of Krivelevich and Sudakov. We use in a novel way a variety of methods, such as a robust Pósa rotation-extension technique, the Friedman-Pippenger tree embedding with rollbacks and the absorbing method, combined with additional tools and ideas.</div><div>Our results have several interesting applications. In particular, they imply the currently best-known bounds on the number of generators which guarantee the Hamiltonicity of random Cayley graphs, which is an important partial case of the well known Hamiltonicity conjecture of Lovász. They can also be used to improve a result of Alon and Bourgain on additive patterns in multiplicative subgroups.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Spectral invariants over the integers","authors":"Yusuke Kawamoto , Egor Shelukhin","doi":"10.1016/j.aim.2024.109976","DOIUrl":"10.1016/j.aim.2024.109976","url":null,"abstract":"<div><div>Spectral invariants are quantitative measurements in symplectic topology coming from Floer homology theory. We study their dependence on the choice of coefficients in the context of Hamiltonian Floer homology. We discover phenomena in this setting which hold for <span><math><mi>Z</mi></math></span>-coefficients and fail for all field coefficients. For example, we prove that the spectral norm, an important metric derived from spectral invariants, is unbounded over <span><math><mi>Z</mi></math></span> for complex projective spaces, while it is uniformly bounded over all fields. This allows us to answer a symplectic version of a question of Hingston, originally asked in the setting of the energy functional on the loop space. We also provide applications to Hamiltonian dynamics and Hofer's geometry.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142532265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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