Journal of Number Theory最新文献_第2页

Modularity of tadpole Nahm sums in ranks 4 and 5 4、5级蝌蚪Nahm和的模性

IF 0.7 3区数学

Journal of Number Theory Pub Date : 2026-07-01 Epub Date: 2026-02-04 DOI: 10.1016/j.jnt.2025.12.010

Changsong Shi, Liuquan Wang

引用次数: 0

Finiteness criteria for the solutions of a sequence of decomposable form inequalities 可分解形式不等式序列解的有限准则

IF 0.7 3区数学

Journal of Number Theory Pub Date : 2026-07-01 Epub Date: 2026-02-03 DOI: 10.1016/j.jnt.2026.01.001

Si Duc Quang

引用次数: 0

Brauer and Néron-Severi groups of surfaces over finite fields 有限域上的Brauer和nsamron - severi群曲面

IF 0.7 3区数学

Journal of Number Theory Pub Date : 2026-07-01 Epub Date: 2026-01-20 DOI: 10.1016/j.jnt.2025.12.004

Thomas H. Geisser

引用次数: 0

Two dimensional integral representations via branches of the Bruhat-Tits tree 通过Bruhat-Tits树分支的二维积分表示

IF 0.7 3区数学

Journal of Number Theory Pub Date : 2026-07-01 Epub Date: 2026-01-21 DOI: 10.1016/j.jnt.2025.12.005

Bruno Aguiló-Vidal , Luis Arenas-Carmona , Matías Saavedra-Lagos

引用次数: 0

On a problem of minimal additive complements of integers 关于整数的最小可加补问题

IF 0.7 3区数学

Journal of Number Theory Pub Date : 2026-07-01 Epub Date: 2026-02-03 DOI: 10.1016/j.jnt.2025.12.012

Wu-Xia Ma , Yong-Gao Chen

{"title":"On a problem of minimal additive complements of integers","authors":"Wu-Xia Ma , Yong-Gao Chen","doi":"10.1016/j.jnt.2025.12.012","DOIUrl":"10.1016/j.jnt.2025.12.012","url":null,"abstract":"<div><h3>Text</h3><div>Let <em>W</em> be a non-empty subset of <span><math><mi>Z</mi></math></span>. A set <span><math><mi>C</mi><mo>⊆</mo><mi>Z</mi></math></span> is called an additive complement to <em>W</em> if <span><math><mi>C</mi><mo>+</mo><mi>W</mi><mo>=</mo><mi>Z</mi></math></span>. An additive complement <em>C</em> is said to be minimal if no proper subset of <em>C</em> is an additive complement to <em>W</em>. In 2019, Kiss, Sándor, and Yang proved that if <em>m</em> is a positive integer and <span><math><mi>W</mi><mo>=</mo><mo>(</mo><mi>m</mi><mi>N</mi><mo>+</mo><mi>X</mi><mo>)</mo><mo>∪</mo><mi>Y</mi></math></span>, where <em>X</em> and <em>Y</em> are finite sets that satisfy certain conditions, then <em>W</em> has a minimal additive complement. They asked whether this is true if <em>Y</em> is an infinite set and does not contain an arithmetic progression of common difference <em>m</em>. In this paper, we present some results on this problem and pose three open problems for further research.</div></div><div><h3>Video</h3><div>For a video summary of this paper, please visit <span><span>https://youtu.be/eSZCqS99au0</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"284 ","pages":"Pages 178-187"},"PeriodicalIF":0.7,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190616","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

Partition-theoretic model of prime distribution 素数分布的划分理论模型

IF 0.7 3区数学

Journal of Number Theory Pub Date : 2026-07-01 Epub Date: 2026-01-21 DOI: 10.1016/j.jnt.2025.12.008

Aidan Botkin , Madeline L. Dawsey , David J. Hemmer , Matthew R. Just , Robert Schneider

{"title":"Partition-theoretic model of prime distribution","authors":"Aidan Botkin , Madeline L. Dawsey , David J. Hemmer , Matthew R. Just , Robert Schneider","doi":"10.1016/j.jnt.2025.12.008","DOIUrl":"10.1016/j.jnt.2025.12.008","url":null,"abstract":"<div><div>We make an application of ideas from partition theory to a problem in multiplicative number theory. We propose a deterministic model of prime number distribution, from first principles related to properties of integer partitions, that naturally predicts the prime number theorem as well as the twin prime conjecture. The model posits that, for <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span>,<span><span><span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msub><mspace></mspace><mo>=</mo><mspace></mspace><mn>1</mn><mspace></mspace><mo>+</mo><mspace></mspace><mn>2</mn><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></munderover><mrow><mo>⌈</mo><mfrac><mrow><mi>d</mi><mo>(</mo><mi>j</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌉</mo></mrow><mspace></mspace><mo>+</mo><mspace></mspace><mi>ε</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>,</mo></math></span></span></span> where <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> is the <em>k</em>th prime number, <span><math><mi>d</mi><mo>(</mo><mi>k</mi><mo>)</mo></math></span> is the divisor function, and <span><math><mi>ε</mi><mo>(</mo><mi>k</mi><mo>)</mo></math></span> is an explicit error term that is negligible asymptotically; both the main term and error term represent enumerative functions in our conceptual model. We refine the error term to give numerical estimates of <span><math><mi>π</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> similar to those provided by the logarithmic integral, and much more accurate than <span><math><mi>li</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> up to <span><math><mi>n</mi><mo>=</mo><mn>10</mn><mo>,</mo><mn>000</mn></math></span> where the estimates are <em>almost exact</em>. We then perform computational tests of unusual predictions of the model, finding limited evidence of predictable variations in prime gaps.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"284 ","pages":"Pages 104-130"},"PeriodicalIF":0.7,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190682","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

Combinatorial invariants for certain classes of non-abelian groups 一类非贝尔群的组合不变量

IF 0.7 3区数学

Journal of Number Theory Pub Date : 2026-06-01 Epub Date: 2025-12-29 DOI: 10.1016/j.jnt.2025.11.011

Naveen K. Godara , Renu Joshi , Eshita Mazumdar

引用次数: 0

Zagier duality for Jacobi forms 雅可比形式的Zagier对偶

IF 0.7 3区数学

Journal of Number Theory Pub Date : 2026-06-01 Epub Date: 2025-12-29 DOI: 10.1016/j.jnt.2025.11.010

Yeong-Wook Kwon , Subong Lim

引用次数: 0

Sharper bounds for the error in the prime number theorem assuming the Riemann Hypothesis 假设黎曼假设，质数定理中误差的更清晰界限

IF 0.7 3区数学

Journal of Number Theory Pub Date : 2026-06-01 Epub Date: 2026-01-20 DOI: 10.1016/j.jnt.2025.12.003

Ethan Simpson Lee , Paweł Nosal

引用次数: 0

A triple convolution sum of the divisor function 除数函数的三重卷积和

IF 0.7 3区数学

Journal of Number Theory Pub Date : 2026-06-01 Epub Date: 2025-12-29 DOI: 10.1016/j.jnt.2025.11.014

Bikram Misra , M. Ram Murty , Biswajyoti Saha

{"title":"A triple convolution sum of the divisor function","authors":"Bikram Misra , M. Ram Murty , Biswajyoti Saha","doi":"10.1016/j.jnt.2025.11.014","DOIUrl":"10.1016/j.jnt.2025.11.014","url":null,"abstract":"<div><div>We study the triple convolution sum of the divisor function given by<span><span><span><math><munder><mo>∑</mo><mrow><mi>n</mi><mo>≤</mo><mi>x</mi></mrow></munder><mi>d</mi><mo>(</mo><mi>n</mi><mo>)</mo><mi>d</mi><mo>(</mo><mi>n</mi><mo>−</mo><mi>h</mi><mo>)</mo><mi>d</mi><mo>(</mo><mi>n</mi><mo>+</mo><mi>h</mi><mo>)</mo></math></span></span></span> for <span><math><mi>h</mi><mo>≠</mo><mn>0</mn></math></span> where <span><math><mi>d</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> denotes the number of positive divisors of <em>n</em>. Based on some algebraic and geometric considerations, Browning conjectured that the above sum is asymptotic to <span><math><msub><mrow><mi>c</mi></mrow><mrow><mi>h</mi></mrow></msub><mi>x</mi><msup><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>x</mi><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msup></math></span>, for a suitable constant <span><math><msub><mrow><mi>c</mi></mrow><mrow><mi>h</mi></mrow></msub><mo>≠</mo><mn>0</mn></math></span>, as <span><math><mi>x</mi><mo>→</mo><mo>∞</mo></math></span>. This conjecture is still unproved. Using sieve-theoretic results of Wolke and Nair (respectively), it is possible to derive the exact order of the sum. The lower bound of the correct order of magnitude can also be derived by very elementary arguments. In this article, using the Tauberian theory for multiple Dirichlet series, we prove an explicit lower bound and provide a new theoretical framework to predict Browning's conjectured constant <span><math><msub><mrow><mi>c</mi></mrow><mrow><mi>h</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"283 ","pages":"Pages 97-120"},"PeriodicalIF":0.7,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927959","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