Advances in Mathematics最新文献

The McKay–Navarro conjecture for the prime 2 质数2的McKay-Navarro猜想

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-05-30 DOI: 10.1016/j.aim.2025.110369

L. Ruhstorfer , A.A. Schaeffer Fry

引用次数: 0

K-theoretic Tate-Poitou duality at prime 2 素数2处的k -理论态点对偶性

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-05-30 DOI: 10.1016/j.aim.2025.110370

Myungsin Cho

引用次数: 0

Proofs of Mizuno's conjectures on rank three Nahm sums of index (1,2,2) Mizuno猜想关于指数（1,2,2）的3阶Nahm和的证明

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-05-28 DOI: 10.1016/j.aim.2025.110368

Boxue Wang, Liuquan Wang

引用次数: 0

Weight representations of affine Kac-Moody algebras and small quantum groups 仿射Kac-Moody代数和小量子群的权表示

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-05-28 DOI: 10.1016/j.aim.2025.110365

Tomoyuki Arakawa , Thomas Creutzig , Kazuya Kawasetsu

引用次数: 0

Newman's conjecture for the partition function modulo integers with at least two distinct prime divisors 具有至少两个不同质因数的配分函数模整数的纽曼猜想

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-05-27 DOI: 10.1016/j.aim.2025.110367

Dohoon Choi , Youngmin Lee

{"title":"Newman's conjecture for the partition function modulo integers with at least two distinct prime divisors","authors":"Dohoon Choi , Youngmin Lee","doi":"10.1016/j.aim.2025.110367","DOIUrl":"10.1016/j.aim.2025.110367","url":null,"abstract":"<div><div>Let <em>M</em> be a positive integer and <span><math><mi>p</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> be the number of partitions of a positive integer <em>n</em>. Newman's Conjecture asserts that for each integer <em>r</em>, there are infinitely many positive integers <em>n</em> such that<span><span><span><math><mi>p</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>≡</mo><mi>r</mi><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mi>M</mi><mo>)</mo><mo>.</mo></math></span></span></span> For a positive integer <em>d</em>, let <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>d</mi></mrow></msub></math></span> be the set of positive integers <em>M</em> such that the number of prime divisors of <em>M</em> is <em>d</em>. In this paper, we prove that for each positive integer <em>d</em>, the density of the set of positive integers <em>M</em> for which Newman's Conjecture holds in <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>d</mi></mrow></msub></math></span> is 1. Furthermore, we study an analogue of Newman's Conjecture for weakly holomorphic modular forms on <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>N</mi><mo>)</mo></math></span> with nebentypus, and this applies to <em>t</em>-core partitions and generalized Frobenius partitions with <em>h</em>-colors.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"477 ","pages":"Article 110367"},"PeriodicalIF":1.5,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144138678","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}

引用次数: 0

The linear stability of non-Kähler Calabi-Yau metrics non-Kähler Calabi-Yau度规的线性稳定性

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-05-26 DOI: 10.1016/j.aim.2025.110366

Kuan-Hui Lee

引用次数: 0

Tame maximal weights, relative types and valuations 驯服最大权重、相对类型和估值

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-05-26 DOI: 10.1016/j.aim.2025.110364

Shijie Bao , Qi'an Guan , Zhitong Mi , Zheng Yuan

{"title":"Tame maximal weights, relative types and valuations","authors":"Shijie Bao , Qi'an Guan , Zhitong Mi , Zheng Yuan","doi":"10.1016/j.aim.2025.110364","DOIUrl":"10.1016/j.aim.2025.110364","url":null,"abstract":"<div><div>In this article, we obtain a class of tame maximal weights (Zhou weights). Using Tian functions (the function of jumping numbers with respect to the exponents of a holomorphic function or the multiples of a plurisubharmonic function) as a main tool, we establish an expression of relative types (Zhou numbers) to these tame maximal weights in integral form, which shows that the relative types satisfy tropical multiplicativity and tropical additivity. Thus, the relative types to Zhou weights are valuations (Zhou valuations) on the ring of germs of holomorphic functions. We use Tian functions and Zhou numbers to measure the singularities of plurisubharmonic functions, involving jumping numbers and multiplier ideal sheaves. Especially, the relative types to Zhou weights characterize the division relations of the ring of germs of holomorphic functions. Finally, we consider a global version of Zhou weights on domains in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, which is a generalization of the pluricomplex Green functions, and we obtain some properties of them, including continuity and some approximation results.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"477 ","pages":"Article 110364"},"PeriodicalIF":1.5,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144134706","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}

引用次数: 0

Characteristic forms of complex Cartan geometries II 复杂卡坦几何的特征形式2

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-05-26 DOI: 10.1016/j.aim.2025.110360

Benjamin McKay

引用次数: 0

Vojta's abc conjecture for algebraic tori and applications over function fields 代数环面上Vojta的abc猜想及其在函数域上的应用

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-05-23 DOI: 10.1016/j.aim.2025.110358

Ji Guo , Khoa D. Nguyen , Chia-Liang Sun , Julie Tzu-Yueh Wang

{"title":"Vojta's abc conjecture for algebraic tori and applications over function fields","authors":"Ji Guo , Khoa D. Nguyen , Chia-Liang Sun , Julie Tzu-Yueh Wang","doi":"10.1016/j.aim.2025.110358","DOIUrl":"10.1016/j.aim.2025.110358","url":null,"abstract":"<div><div>We prove Vojta's generalized abc conjecture for algebraic tori over function fields with exceptional sets that can be determined effectively. Additionally, we establish a version of the conjecture for toric varieties. As an application, we investigate the Lang-Vojta Conjecture for varieties of log general type that are ramified covers of <span><math><msubsup><mrow><mi>G</mi></mrow><mrow><mi>m</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> over function fields. In particular, we consider the case of <span><math><msup><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>∖</mo><mi>D</mi></math></span>, where <em>D</em> is a hypersurface over a function field in <span><math><msup><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> with <span><math><mi>n</mi><mo>+</mo><mn>1</mn></math></span> irreducible components and <span><math><mi>deg</mi><mo>⁡</mo><mi>D</mi><mo>≥</mo><mi>n</mi><mo>+</mo><mn>2</mn></math></span>. Our methods also apply to the complex situation, enabling us to find explicit exceptional sets for the corresponding case of Vojta's general abc conjecture (complex version) and the Green-Griffiths-Lang conjecture.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"476 ","pages":"Article 110358"},"PeriodicalIF":1.5,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144115047","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}

引用次数: 0

On global smooth solutions to the 2D isentropic and irrotational Chaplygin gases with short pulse data 二维等熵无旋Chaplygin气体短脉冲数据的全局光滑解

IF 1.5 1区数学

Advances in Mathematics Pub Date : 2025-05-23 DOI: 10.1016/j.aim.2025.110362

Bingbing Ding , Zhouping Xin , Huicheng Yin

引用次数: 0