Pub Date : 2024-11-20DOI: 10.1016/j.jnt.2024.10.009
Ilaria Viglino
We study the distributions of the splitting primes in certain families of number fields. The first and main example is the family of polynomials monic of degree n with height less or equal then N, and then let N go to infinity. We prove an average version of the Chebotarev Density Theorem for this family. In particular, this gives a Central Limit Theorem for the number of primes with given splitting type in some ranges. As an application, we deduce some estimates for the ℓ-torsion in the class groups and for the average of ramified primes.
{"title":"Arithmetic statistics of families of integer Sn-polynomials and application to class group torsion","authors":"Ilaria Viglino","doi":"10.1016/j.jnt.2024.10.009","DOIUrl":"10.1016/j.jnt.2024.10.009","url":null,"abstract":"<div><div>We study the distributions of the splitting primes in certain families of number fields. The first and main example is the family <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>N</mi></mrow></msub></math></span> of polynomials <span><math><mi>f</mi><mo>∈</mo><mi>Z</mi><mo>[</mo><mi>X</mi><mo>]</mo></math></span> monic of degree <em>n</em> with height less or equal then <em>N</em>, and then let <em>N</em> go to infinity. We prove an average version of the Chebotarev Density Theorem for this family. In particular, this gives a Central Limit Theorem for the number of primes with given splitting type in some ranges. As an application, we deduce some estimates for the <em>ℓ</em>-torsion in the class groups and for the average of ramified primes.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"271 ","pages":"Pages 33-65"},"PeriodicalIF":0.6,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-20DOI: 10.1016/j.jnt.2024.08.008
Khai-Hoan Nguyen-Dang
Let p be a rational prime number, let K denote a finite extension of , some fixed algebraic closure of K. Let be the absolute Galois group of K and let be its inertial subgroup. Let A be an Abelian variety defined over K, with semi-stable reduction. In this note, we give a criterion for which , where is the p-adic Tate module associated to A.
{"title":"Galois actions on Tate modules of Abelian varieties with semi-stable reduction","authors":"Khai-Hoan Nguyen-Dang","doi":"10.1016/j.jnt.2024.08.008","DOIUrl":"10.1016/j.jnt.2024.08.008","url":null,"abstract":"<div><div>Let <em>p</em> be a rational prime number, let <em>K</em> denote a finite extension of <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>, <span><math><mover><mrow><mi>K</mi></mrow><mo>‾</mo></mover></math></span> some fixed algebraic closure of <em>K</em>. Let <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>K</mi></mrow></msub></math></span> be the absolute Galois group of <em>K</em> and let <span><math><msub><mrow><mi>I</mi></mrow><mrow><mi>K</mi></mrow></msub><mo>⊂</mo><msub><mrow><mi>G</mi></mrow><mrow><mi>K</mi></mrow></msub></math></span> be its inertial subgroup. Let <em>A</em> be an Abelian variety defined over <em>K</em>, with semi-stable reduction. In this note, we give a criterion for which <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>p</mi></mrow></msub><msup><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mrow><msub><mrow><mi>I</mi></mrow><mrow><mi>K</mi></mrow></msub></mrow></msup><mo>=</mo><mn>0</mn></math></span>, where <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo></math></span> is the <em>p</em>-adic Tate module associated to <em>A</em>.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"269 ","pages":"Pages 247-259"},"PeriodicalIF":0.6,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744085","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}
Pub Date : 2024-11-20DOI: 10.1016/j.jnt.2024.10.005
Saad El Boukhari
Let be a finite abelian extension of number fields of Galois group G with k imaginary quadratic. Let be a rational integer, and for a certain finite set S of places of k, let be the ring of S-integers of K. We use generalized Stark elements to construct first order Stickelberger modules in odd higher algebraic K-groups of . We show that the Fitting ideal (resp. index) of these modules inside the corresponding odd K-groups is exactly the Fitting ideal (resp. cardinality) of the even higher algebraic K-group .
{"title":"First order Stickelberger modules over imaginary quadratic fields","authors":"Saad El Boukhari","doi":"10.1016/j.jnt.2024.10.005","DOIUrl":"10.1016/j.jnt.2024.10.005","url":null,"abstract":"<div><div>Let <span><math><mi>K</mi><mo>/</mo><mi>k</mi></math></span> be a finite abelian extension of number fields of Galois group <em>G</em> with <em>k</em> imaginary quadratic. Let <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span> be a rational integer, and for a certain finite set <em>S</em> of places of <em>k</em>, let <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>K</mi><mo>,</mo><mi>S</mi></mrow></msub></math></span> be the ring of <em>S</em>-integers of <em>K</em>. We use generalized Stark elements to construct first order Stickelberger modules in odd higher algebraic <em>K</em>-groups of <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>K</mi><mo>,</mo><mi>S</mi></mrow></msub></math></span>. We show that the Fitting ideal (resp. index) of these modules inside the corresponding odd <em>K</em>-groups is exactly the Fitting ideal (resp. cardinality) of the even higher algebraic <em>K</em>-group <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>2</mn><mi>n</mi><mo>−</mo><mn>2</mn></mrow></msub><mo>(</mo><msub><mrow><mi>O</mi></mrow><mrow><mi>K</mi><mo>,</mo><mi>S</mi></mrow></msub><mo>)</mo></math></span>.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"269 ","pages":"Pages 1-16"},"PeriodicalIF":0.6,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744126","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}
Pub Date : 2024-11-20DOI: 10.1016/j.jnt.2024.10.008
Sebastian Monnet
Given a 2-adic field K, we give a formula for the number of totally ramified quartic field extensions with a given discriminant valuation and Galois closure group. We use these formulae to prove refinements of Serre's mass formula, which will have applications to the arithmetic statistics of number fields.
{"title":"Counting wild quartics with prescribed discriminant and Galois closure group","authors":"Sebastian Monnet","doi":"10.1016/j.jnt.2024.10.008","DOIUrl":"10.1016/j.jnt.2024.10.008","url":null,"abstract":"<div><div>Given a 2-adic field <em>K</em>, we give a formula for the number of totally ramified quartic field extensions <span><math><mi>L</mi><mo>/</mo><mi>K</mi></math></span> with a given discriminant valuation and Galois closure group. We use these formulae to prove refinements of Serre's mass formula, which will have applications to the arithmetic statistics of number fields.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"269 ","pages":"Pages 157-202"},"PeriodicalIF":0.6,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-20DOI: 10.1016/j.jnt.2024.09.015
Ernst-Ulrich Gekeler
We study expansions of Drinfeld modular forms of rank along the boundary of moduli varieties. Product formulas for the discriminant forms are developed, which are analogous with Jacobi's formula for the classical elliptic discriminant. The vanishing orders are described through values at of partial zeta functions of the underlying Drinfeld coefficient ring A. We show linear independence properties for Eisenstein series, which allow to split spaces of modular forms into the subspaces of cusp forms and of Eisenstein series, and give various characterizations of the boundary condition for modular forms.
{"title":"On Drinfeld modular forms of higher rank VII: Expansions at the boundary","authors":"Ernst-Ulrich Gekeler","doi":"10.1016/j.jnt.2024.09.015","DOIUrl":"10.1016/j.jnt.2024.09.015","url":null,"abstract":"<div><div>We study expansions of Drinfeld modular forms of rank <span><math><mi>r</mi><mo>≥</mo><mn>2</mn></math></span> along the boundary of moduli varieties. Product formulas for the discriminant forms <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> are developed, which are analogous with Jacobi's formula for the classical elliptic discriminant. The vanishing orders are described through values at <span><math><mi>s</mi><mo>=</mo><mn>1</mn><mo>−</mo><mi>r</mi></math></span> of partial zeta functions of the underlying Drinfeld coefficient ring <em>A</em>. We show linear independence properties for Eisenstein series, which allow to split spaces of modular forms into the subspaces of cusp forms and of Eisenstein series, and give various characterizations of the boundary condition for modular forms.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"269 ","pages":"Pages 260-340"},"PeriodicalIF":0.6,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.jnt.2024.10.001
Chiara Bellotti
We will provide an explicit log-free zero-density estimate for of the form . In particular, this estimate becomes the sharpest known explicit zero-density estimate uniformly for , with and .
{"title":"An explicit log-free zero density estimate for the Riemann zeta-function","authors":"Chiara Bellotti","doi":"10.1016/j.jnt.2024.10.001","DOIUrl":"10.1016/j.jnt.2024.10.001","url":null,"abstract":"<div><div>We will provide an explicit log-free zero-density estimate for <span><math><mi>ζ</mi><mo>(</mo><mi>s</mi><mo>)</mo></math></span> of the form <span><math><mi>N</mi><mo>(</mo><mi>σ</mi><mo>,</mo><mi>T</mi><mo>)</mo><mo>≤</mo><mi>A</mi><msup><mrow><mi>T</mi></mrow><mrow><mi>B</mi><mo>(</mo><mn>1</mn><mo>−</mo><mi>σ</mi><mo>)</mo></mrow></msup></math></span>. In particular, this estimate becomes the sharpest known explicit zero-density estimate uniformly for <span><math><mi>σ</mi><mo>∈</mo><mo>[</mo><msub><mrow><mi>α</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><mn>1</mn><mo>]</mo></math></span>, with <span><math><mn>0.985</mn><mo>≤</mo><msub><mrow><mi>α</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≤</mo><mn>0.9927</mn></math></span> and <span><math><mn>3</mn><mo>⋅</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>12</mn></mrow></msup><mo><</mo><mi>T</mi><mo>≤</mo><mi>exp</mi><mo></mo><mo>(</mo><mn>6.7</mn><mo>⋅</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>12</mn></mrow></msup><mo>)</mo></math></span>.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"269 ","pages":"Pages 37-77"},"PeriodicalIF":0.6,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.jnt.2024.10.003
Bing He, Shuming Liu
In this paper, we will study a conjecture of Merca on theta series, which gives a refinement of a conjecture of Andrews and Merca on truncated pentagonal number series. We first show refinements of two special cases of Merca's conjecture and then establish several nonnegativity results on theta series. As applications, we establish positivity results involving two celebrated partition statistics.
{"title":"A conjecture of Merca on nonnegativity of theta series","authors":"Bing He, Shuming Liu","doi":"10.1016/j.jnt.2024.10.003","DOIUrl":"10.1016/j.jnt.2024.10.003","url":null,"abstract":"<div><div>In this paper, we will study a conjecture of Merca on theta series, which gives a refinement of a conjecture of Andrews and Merca on truncated pentagonal number series. We first show refinements of two special cases of Merca's conjecture and then establish several nonnegativity results on theta series. As applications, we establish positivity results involving two celebrated partition statistics.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"269 ","pages":"Pages 17-36"},"PeriodicalIF":0.6,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744195","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}
Pub Date : 2024-11-19DOI: 10.1016/j.jnt.2024.10.002
Francesco Cellarosi , Tariq Osman
We provide explicit families of pairs such that for sufficiently regular f, there is a constant C for which the theta sum bound holds for every and every . Central to the proof is realising that, for fixed N, the theta sum normalised by agrees with an automorphic function evaluated along a special curve known as a horocycle lift. The lift depends on the pair , and so the bound follows from showing that there are pairs such that remains bounded along the entire horocycle lift.
{"title":"Bounds for smooth theta sums with rational parameters","authors":"Francesco Cellarosi , Tariq Osman","doi":"10.1016/j.jnt.2024.10.002","DOIUrl":"10.1016/j.jnt.2024.10.002","url":null,"abstract":"<div><div>We provide explicit families of pairs <span><math><mo>(</mo><mtext>α</mtext><mo>,</mo><mtext>β</mtext><mo>)</mo><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>k</mi></mrow></msup><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>k</mi></mrow></msup></math></span> such that for sufficiently regular <em>f</em>, there is a constant <em>C</em> for which the theta sum bound<span><span><span><math><mrow><mo>|</mo><munder><mo>∑</mo><mrow><mtext>n</mtext><mo>∈</mo><msup><mrow><mi>Z</mi></mrow><mrow><mi>k</mi></mrow></msup></mrow></munder><mi>f</mi><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>N</mi></mrow></mfrac><mrow><mi>n</mi></mrow><mo>)</mo></mrow><mi>exp</mi><mo></mo><mo>{</mo><mn>2</mn><mi>π</mi><mi>i</mi><mo>(</mo><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><msup><mrow><mo>‖</mo><mrow><mi>n</mi></mrow><mo>‖</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mrow><mi>β</mi></mrow><mo>⋅</mo><mrow><mi>n</mi></mrow><mo>)</mo><mi>x</mi><mo>+</mo><mrow><mi>α</mi></mrow><mo>⋅</mo><mrow><mi>n</mi></mrow><mo>)</mo><mo>}</mo><mo>|</mo></mrow><mspace></mspace><mo>≤</mo><mi>C</mi><msup><mrow><mi>N</mi></mrow><mrow><mi>k</mi><mo>/</mo><mn>2</mn></mrow></msup><mo>,</mo></math></span></span></span> holds for every <span><math><mi>x</mi><mo>∈</mo><mi>R</mi></math></span> and every <span><math><mi>N</mi><mo>∈</mo><mi>N</mi></math></span>. Central to the proof is realising that, for fixed <em>N</em>, the theta sum normalised by <span><math><msup><mrow><mi>N</mi></mrow><mrow><mi>k</mi><mo>/</mo><mn>2</mn></mrow></msup></math></span> agrees with an automorphic function <span><math><msub><mrow><mi>Θ</mi></mrow><mrow><mi>f</mi></mrow></msub></math></span> evaluated along a special curve known as a horocycle lift. The lift depends on the pair <span><math><mo>(</mo><mtext>α</mtext><mo>,</mo><mtext>β</mtext><mo>)</mo></math></span>, and so the bound follows from showing that there are pairs such that <span><math><mo>|</mo><msub><mrow><mi>Θ</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>|</mo></math></span> remains bounded along the entire horocycle lift.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"269 ","pages":"Pages 397-426"},"PeriodicalIF":0.6,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744088","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}
Pub Date : 2024-11-06DOI: 10.1016/j.jnt.2024.09.002
Kavita Dhanda, Alan Haynes
Building on classical aspects of the theory of Diophantine approximation, we consider the collection of all accumulation points of normalized integer vector translates of points with and . In the first part of the paper we derive measure theoretic and Hausdorff dimension results about the set of α whose accumulation points are all of . In the second part we focus primarily on the case when the coordinates of α together with 1 form a basis for an algebraic number field K. Here we show that, under the correct normalization, the set of accumulation points displays an ordered geometric structure which reflects algebraic properties of the underlying number field. For example, when , this collection of accumulation points can be described as a countable union of dilates (by norms of elements of an order in K) of a single ellipse, or of a pair of hyperbolas, depending on whether or not K has a non-trivial embedding into .
以二阶近似理论的经典方面为基础，我们考虑了具有 α∈Rd 和 q∈Z 的点 qα 的归一化整数向量平移的所有堆积点的集合。在论文的第一部分，我们推导了关于积点都是 Rd 的 α 集合的度量论和豪斯多夫维度结果。在第二部分中，我们主要关注当 α 的坐标与 1 一起构成代数数域 K 的基础时的情况。我们在此证明，在正确的归一化条件下，累积点集合显示出有序的几何结构，它反映了基础数域的代数特性。例如，当 d=2 时，这个积点集合可以被描述为一个椭圆或一对双曲线的扩张（通过 K 中一个阶元素的规范）的可数联合，这取决于 K 是否有一个非三维嵌入到 C 中。
{"title":"Accumulation points of normalized approximations","authors":"Kavita Dhanda, Alan Haynes","doi":"10.1016/j.jnt.2024.09.002","DOIUrl":"10.1016/j.jnt.2024.09.002","url":null,"abstract":"<div><div>Building on classical aspects of the theory of Diophantine approximation, we consider the collection of all accumulation points of normalized integer vector translates of points <span><math><mi>q</mi><mi>α</mi></math></span> with <span><math><mi>α</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> and <span><math><mi>q</mi><mo>∈</mo><mi>Z</mi></math></span>. In the first part of the paper we derive measure theoretic and Hausdorff dimension results about the set of <strong><em>α</em></strong> whose accumulation points are all of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>. In the second part we focus primarily on the case when the coordinates of <strong><em>α</em></strong> together with 1 form a basis for an algebraic number field <em>K</em>. Here we show that, under the correct normalization, the set of accumulation points displays an ordered geometric structure which reflects algebraic properties of the underlying number field. For example, when <span><math><mi>d</mi><mo>=</mo><mn>2</mn></math></span>, this collection of accumulation points can be described as a countable union of dilates (by norms of elements of an order in <em>K</em>) of a single ellipse, or of a pair of hyperbolas, depending on whether or not <em>K</em> has a non-trivial embedding into <span><math><mi>C</mi></math></span>.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"268 ","pages":"Pages 1-38"},"PeriodicalIF":0.6,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142699240","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}
Pub Date : 2024-11-05DOI: 10.1016/j.jnt.2024.09.006
Florian Luca , István Pink
In this paper, we find all the solutions of the Diophantine equation from the title.
在本文中，我们将从题目中找出 Diophantine 方程的所有解。
{"title":"On the Diophantine equation 2s + pk = m2 with a Fermat prime p","authors":"Florian Luca , István Pink","doi":"10.1016/j.jnt.2024.09.006","DOIUrl":"10.1016/j.jnt.2024.09.006","url":null,"abstract":"<div><div>In this paper, we find all the solutions of the Diophantine equation from the title.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"268 ","pages":"Pages 49-71"},"PeriodicalIF":0.6,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142699242","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}
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