Journal of Number Theory最新文献

Corrigendum to: “A Lehmer-type lower bound for the canonical height on elliptic curves over function fields” [J. Number Theory 262 (2024) 506–538] “函数场上椭圆曲线正则高度的lehmer型下界”的更正[J]。数论262 (2024)506-538]

IF 0.6 3区数学

Journal of Number Theory Pub Date : 2025-07-25 DOI: 10.1016/j.jnt.2025.06.016

Joseph H. Silverman

引用次数: 0

Poissonian pair correlation of linear generalized monomials over primes 素数上线性广义单项式的泊松对相关

IF 0.6 3区数学

Journal of Number Theory Pub Date : 2025-07-22 DOI: 10.1016/j.jnt.2025.06.012

C.G. Karthick Babu , E. Malavika , G.K. Viswanadham

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Bol's identity for skew-holomorphic Jacobi forms 斜全纯Jacobi形式的Bol恒等式

IF 0.6 3区数学

Journal of Number Theory Pub Date : 2025-07-21 DOI: 10.1016/j.jnt.2025.06.015

Youngmin Lee , Subong Lim

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Towards the Fontaine-Mazur conjecture for biquadratic extensions: An example 关于双二次扩展的Fontaine-Mazur猜想：一个例子

IF 0.7 3区数学

Journal of Number Theory Pub Date : 2025-07-21 DOI: 10.1016/j.jnt.2025.06.005

Ramla Abdellatif , Supriya Pisolkar

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On Bass' conjecture of the small Davenport constant 关于Bass关于小达文波特常数的猜想

IF 0.7 3区数学

Journal of Number Theory Pub Date : 2025-07-21 DOI: 10.1016/j.jnt.2025.06.009

Guoqing Wang, Yang Zhao

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The generalized linear period and the Shalika period over a division algebra 除法代数上的广义线性周期和Shalika周期

IF 0.6 3区数学

Journal of Number Theory Pub Date : 2025-07-21 DOI: 10.1016/j.jnt.2025.06.013

Hengfei Lu

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A simple proof of a reverse Minkowski theorem for integral lattices 积分格的反闵可夫斯基定理的一个简单证明

IF 0.6 3区数学

Journal of Number Theory Pub Date : 2025-07-21 DOI: 10.1016/j.jnt.2025.06.014

Oded Regev , Noah Stephens-Davidowitz

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Remarks on p-primary torsion of the Brauer group 关于Brauer群的p-初级扭转的注释

IF 0.6 3区数学

Journal of Number Theory Pub Date : 2025-07-21 DOI: 10.1016/j.jnt.2025.06.003

Yuan Yang

{"title":"Remarks on p-primary torsion of the Brauer group","authors":"Yuan Yang","doi":"10.1016/j.jnt.2025.06.003","DOIUrl":"10.1016/j.jnt.2025.06.003","url":null,"abstract":"<div><div>For a smooth and proper variety X over an algebraically closed field k of characteristic <math><mi>p</mi><mo>></mo><mn>0</mn></math>, the group <math><mrow><mi>Br</mi></mrow><mo>(</mo><mi>X</mi><mo>)</mo><mo>[</mo><msup><mrow><mi>p</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>]</mo></math> is a direct sum of finitely many copies of <math><msub><mrow><mi>Q</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>/</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub></math> and <math><msup><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>(</mo><mi>X</mi><mo>,</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mn>1</mn><mo>)</mo><mo>)</mo><mo>[</mo><msup><mrow><mi>p</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>]</mo></math>, an abelian group of finite exponent. The latter is an extension of a finite group J by the group of k-points of a connected commutative unipotent algebraic group U. In this paper we show that (1) if X is ordinary, then <math><mi>U</mi><mo>=</mo><mn>0</mn></math>; (2) if X is a surface, then J is the Pontryagin dual of <math><mrow><mi>NS</mi></mrow><mo>(</mo><mi>X</mi><mo>)</mo><mo>[</mo><msup><mrow><mi>p</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>]</mo></math>; (3) if X is an abelian variety, then <math><mi>J</mi><mo>=</mo><mn>0</mn></math>. Using Crew's formula and Ekedahl's inequality, we compute the dimension of U for surfaces and for abelian 3-folds. We show that, if X is ordinary, then the unipotent subgroup of <math><mrow><mi>Br</mi></mrow><mo>(</mo><mi>X</mi><mo>×</mo><mi>Y</mi><mo>)</mo></math> is isomorphic to the unipotent subgroup of <math><mrow><mi>Br</mi></mrow><mo>(</mo><mi>Y</mi><mo>)</mo></math>. Generalizing a result of Ogus, we give a criterion for the injectivity of the canonical map from flat to crystalline cohomology in degree 2.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"279 ","pages":"Pages 184-215"},"PeriodicalIF":0.6,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144687069","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}

引用次数: 0

Asymptotic variation of elementary abelian p-extensions over P1 P1上初等阿贝尔p扩展的渐近变分

IF 0.7 3区数学

Journal of Number Theory Pub Date : 2025-07-21 DOI: 10.1016/j.jnt.2025.06.004

Hui June Zhu

引用次数: 0

Iwasawa theory for Rankin-Selberg product at an Eisenstein prime 爱森斯坦素数下Rankin-Selberg积的Iwasawa理论

IF 0.7 3区数学

Journal of Number Theory Pub Date : 2025-07-21 DOI: 10.1016/j.jnt.2025.06.007

Somnath Jha , Sudhanshu Shekhar , Ravitheja Vangala

{"title":"Iwasawa theory for Rankin-Selberg product at an Eisenstein prime","authors":"Somnath Jha , Sudhanshu Shekhar , Ravitheja Vangala","doi":"10.1016/j.jnt.2025.06.007","DOIUrl":"10.1016/j.jnt.2025.06.007","url":null,"abstract":"<div><div>Let p be an odd prime, f be a p-ordinary newform of weight k and h be a normalized cuspidal p-ordinary Hecke eigenform of weight <math><mi>l</mi><mo><</mo><mi>k</mi></math>. In this article, we study the p-adic L-function and <math><msup><mrow><mi>p</mi></mrow><mrow><mo>∞</mo></mrow></msup></math>-Selmer group of the Rankin-Selberg product of f and h under the assumption that p is an Eisenstein prime for h i.e. the residual Galois representation of h at p is reducible. We show that the p-adic L-function and the characteristic ideal of the <math><msup><mrow><mi>p</mi></mrow><mrow><mo>∞</mo></mrow></msup></math>-Selmer group of the Rankin-Selberg product of <math><mi>f</mi><mo>,</mo><mi>h</mi></math> generate the same ideal modulo p in the Iwasawa algebra i.e. the Rankin-Selberg Iwasawa main conjecture for <math><mi>f</mi><mo>⊗</mo><mi>h</mi></math> holds mod p. As an application to our results, we explicitly describe a few examples where the above congruence holds.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"279 ","pages":"Pages 348-410"},"PeriodicalIF":0.7,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724475","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}

引用次数: 0