Research in Number Theory最新文献

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A note on badly approximable systems of linear forms over a field of formal series 关于形式级数域上线性形式的严重近似系统的注释
IF 0.8
Research in Number Theory Pub Date : 2023-04-15 DOI: 10.1007/s40993-023-00437-x
Mumtaz Hussain, N. Shulga
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引用次数: 0
On the Iwasawa invariants of prime cyclotomic fields 素数分环场的Iwasawa不变量
IF 0.8
Research in Number Theory Pub Date : 2023-04-11 DOI: 10.1007/s40993-023-00435-z
Sey Y. Kim
{"title":"On the Iwasawa invariants of prime cyclotomic fields","authors":"Sey Y. Kim","doi":"10.1007/s40993-023-00435-z","DOIUrl":"https://doi.org/10.1007/s40993-023-00435-z","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"15 1","pages":"1-20"},"PeriodicalIF":0.8,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79099814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the adjoint of higher order Serre derivatives 关于高阶Serre导数的伴随函数
IF 0.8
Research in Number Theory Pub Date : 2023-04-11 DOI: 10.1007/s40993-023-00438-w
M. Charan
{"title":"On the adjoint of higher order Serre derivatives","authors":"M. Charan","doi":"10.1007/s40993-023-00438-w","DOIUrl":"https://doi.org/10.1007/s40993-023-00438-w","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"15 1","pages":"1-8"},"PeriodicalIF":0.8,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85021942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Identities associated to a generalized divisor function and modified Bessel function 广义除数函数和修正贝塞尔函数的恒等式
IF 0.8
Research in Number Theory Pub Date : 2023-03-31 DOI: 10.1007/s40993-023-00431-3
D. Banerjee, B. Maji
{"title":"Identities associated to a generalized divisor function and modified Bessel function","authors":"D. Banerjee, B. Maji","doi":"10.1007/s40993-023-00431-3","DOIUrl":"https://doi.org/10.1007/s40993-023-00431-3","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"15 1","pages":"1-29"},"PeriodicalIF":0.8,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89071851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Modular forms on $${{,textrm{SU},}}(2,1)$$ with weight $$frac{1}{3}$$ 模块形式在$${{,textrm{SU},}}(2,1)$$与重量 $$frac{1}{3}$$
IF 0.8
Research in Number Theory Pub Date : 2023-03-28 DOI: 10.1007/s40993-022-00361-6
E. Freitag, Richard M. Hill
{"title":"Modular forms on $${{,textrm{SU},}}(2,1)$$ with weight $$frac{1}{3}$$","authors":"E. Freitag, Richard M. Hill","doi":"10.1007/s40993-022-00361-6","DOIUrl":"https://doi.org/10.1007/s40993-022-00361-6","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"38 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87504722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A note on Halász’s Theorem in Fq[t]documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${mathbb {F}}_q[t]$$end{document} A note on Halász’s Theorem in Fq[t]documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${mathbb {F}}_q[t]$$end{document}
IF 0.8
Research in Number Theory Pub Date : 2023-03-22 DOI: 10.1007/s40993-023-00432-2
Ardavan Afshar
{"title":"A note on Halász’s Theorem in Fq[t]documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${mathbb {F}}_q[t]$$end{document}","authors":"Ardavan Afshar","doi":"10.1007/s40993-023-00432-2","DOIUrl":"https://doi.org/10.1007/s40993-023-00432-2","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"67 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74852808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The probability of non-isomorphic group structures of isogenous elliptic curves in finite field extensions, I 有限域扩展中等均椭圆曲线非同构群结构的概率
IF 0.8
Research in Number Theory Pub Date : 2023-01-22 DOI: 10.1007/s40993-023-00456-8
J. Cullinan, N. Kaplan
{"title":"The probability of non-isomorphic group structures of isogenous elliptic curves in finite field extensions, I","authors":"J. Cullinan, N. Kaplan","doi":"10.1007/s40993-023-00456-8","DOIUrl":"https://doi.org/10.1007/s40993-023-00456-8","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"57 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72830781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unlikely intersections on the p-adic formal ball. p进正式球上不可能的交集。
IF 0.8
Research in Number Theory Pub Date : 2023-01-01 DOI: 10.1007/s40993-023-00441-1
Vlad Serban
{"title":"Unlikely intersections on the <i>p</i>-adic formal ball.","authors":"Vlad Serban","doi":"10.1007/s40993-023-00441-1","DOIUrl":"https://doi.org/10.1007/s40993-023-00441-1","url":null,"abstract":"<p><p>We investigate generalizations along the lines of the Mordell-Lang conjecture of the author's <i>p</i>-adic formal Manin-Mumford results for <i>n</i>-dimensional <i>p</i>-divisible formal groups <math><mi>F</mi></math> . In particular, given a finitely generated subgroup <math><mi>Γ</mi></math> of <math><mrow><mi>F</mi> <mo>(</mo> <msub><mover><mi>Q</mi> <mo>¯</mo></mover> <mi>p</mi></msub> <mo>)</mo></mrow> </math> and a closed subscheme <math><mrow><mi>X</mi> <mo>↪</mo> <mi>F</mi></mrow> </math> , we show under suitable assumptions that for any points <math><mrow><mi>P</mi> <mo>∈</mo> <mi>X</mi> <mo>(</mo> <msub><mi>C</mi> <mi>p</mi></msub> <mo>)</mo></mrow> </math> satisfying <math><mrow><mi>n</mi> <mi>P</mi> <mo>∈</mo> <mi>Γ</mi></mrow> </math> for some <math><mrow><mi>n</mi> <mo>∈</mo> <mi>N</mi></mrow> </math> , the minimal such orders <i>n</i> are uniformly bounded whenever <i>X</i> does not contain a formal subgroup translate of positive dimension. In contrast, we then provide counter-examples to a full <i>p</i>-adic formal Mordell-Lang result. Finally, we outline some consequences for the study of the Zariski-density of sets of automorphic objects in <i>p</i>-adic deformations. Specifically, we do so in the context of the nearly ordinary <i>p</i>-adic families of cuspidal cohomological automorphic forms for the general linear group constructed by Hida.</p>","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"9 2","pages":"34"},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10149481/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9408242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Inequalities for higher order differences of the logarithm of the overpartition function and a problem of Wang-Xie-Zhang. 过配分函数的对数高阶差分不等式及王协章问题。
IF 0.8
Research in Number Theory Pub Date : 2023-01-01 DOI: 10.1007/s40993-022-00420-y
Gargi Mukherjee
{"title":"Inequalities for higher order differences of the logarithm of the overpartition function and a problem of Wang-Xie-Zhang.","authors":"Gargi Mukherjee","doi":"10.1007/s40993-022-00420-y","DOIUrl":"https://doi.org/10.1007/s40993-022-00420-y","url":null,"abstract":"&lt;p&gt;&lt;p&gt;Let &lt;math&gt; &lt;mrow&gt;&lt;mover&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mo&gt;¯&lt;/mo&gt;&lt;/mover&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;n&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/mrow&gt; &lt;/math&gt; denote the overpartition function. In this paper, our primary goal is to study the asymptotic behavior of the finite differences of the logarithm of the overpartition function, i.e., &lt;math&gt; &lt;mrow&gt; &lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mo&gt;-&lt;/mo&gt; &lt;mn&gt;1&lt;/mn&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt; &lt;mo&gt;-&lt;/mo&gt; &lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt; &lt;/msup&gt; &lt;msup&gt;&lt;mi&gt;Δ&lt;/mi&gt; &lt;mi&gt;r&lt;/mi&gt;&lt;/msup&gt; &lt;mo&gt;log&lt;/mo&gt; &lt;mover&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mo&gt;¯&lt;/mo&gt;&lt;/mover&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;n&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/mrow&gt; &lt;/math&gt; , by studying the inequality of the following form &lt;dispformula&gt; &lt;math&gt; &lt;mrow&gt; &lt;mtable&gt; &lt;mtr&gt; &lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;log&lt;/mo&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;/mrow&gt; &lt;mn&gt;1&lt;/mn&gt; &lt;mo&gt;+&lt;/mo&gt; &lt;mstyle&gt; &lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt; &lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;r&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt; &lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt; &lt;mo&gt;-&lt;/mo&gt; &lt;mn&gt;1&lt;/mn&gt; &lt;mo&gt;/&lt;/mo&gt; &lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt; &lt;/msup&gt; &lt;/mfrac&gt; &lt;/mstyle&gt; &lt;mo&gt;-&lt;/mo&gt; &lt;mstyle&gt; &lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt; &lt;mo&gt;+&lt;/mo&gt; &lt;msub&gt;&lt;mi&gt;C&lt;/mi&gt; &lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;r&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/mrow&gt; &lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt; &lt;mi&gt;r&lt;/mi&gt;&lt;/msup&gt; &lt;/mfrac&gt; &lt;/mstyle&gt; &lt;mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mrow&gt;&lt;/mrow&gt;&lt;/mrow&gt; &lt;/mtd&gt; &lt;mtd&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;/mrow&gt; &lt;mo&gt;&lt;&lt;/mo&gt; &lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mo&gt;-&lt;/mo&gt; &lt;mn&gt;1&lt;/mn&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt; &lt;mo&gt;-&lt;/mo&gt; &lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt; &lt;/msup&gt; &lt;msup&gt;&lt;mi&gt;Δ&lt;/mi&gt; &lt;mi&gt;r&lt;/mi&gt;&lt;/msup&gt; &lt;mo&gt;log&lt;/mo&gt; &lt;mover&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mo&gt;¯&lt;/mo&gt;&lt;/mover&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;n&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/mrow&gt; &lt;/mtd&gt; &lt;/mtr&gt; &lt;mtr&gt; &lt;mtd&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;/mrow&gt; &lt;mrow&gt;&lt;/mrow&gt; &lt;mrow&gt;&lt;/mrow&gt;&lt;/mrow&gt; &lt;/mtd&gt; &lt;mtd&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;/mrow&gt; &lt;mo&gt;&lt;&lt;/mo&gt; &lt;mo&gt;log&lt;/mo&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;/mrow&gt; &lt;mn&gt;1&lt;/mn&gt; &lt;mo&gt;+&lt;/mo&gt; &lt;mstyle&gt; &lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt; &lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;r&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt; &lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt; &lt;mo&gt;-&lt;/mo&gt; &lt;mn&gt;1&lt;/mn&gt; &lt;mo&gt;/&lt;/mo&gt; &lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt; &lt;/msup&gt; &lt;/mfrac&gt; &lt;/mstyle&gt; &lt;mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mspace&gt;&lt;/mspace&gt; &lt;mtext&gt;for&lt;/mtext&gt; &lt;mspace&gt;&lt;/mspace&gt; &lt;mi&gt;n&lt;/mi&gt; &lt;mo&gt;≥&lt;/mo&gt; &lt;mi&gt;N&lt;/mi&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;r&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt; &lt;/mtd&gt; &lt;/mtr&gt; &lt;/mtable&gt; &lt;/mrow&gt; &lt;/math&gt; &lt;/dispformula&gt; where &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;r&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;msub&gt;&lt;mi&gt;C&lt;/mi&gt; &lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;r&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mtext&gt;and&lt;/mtext&gt; &lt;mspace&gt;&lt;/mspace&gt; &lt;mi&gt;N&lt;/mi&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;r&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/mrow&gt; &lt;/math&gt; are computable constants depending on the positive integer &lt;i&gt;r&lt;/i&gt;, determined explicitly. This solves a problem posed by Wang, Xie and Zhang in the context of searching for a better lower bound of &lt;math&gt; &lt;mrow&gt; &lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mo&gt;-&lt;/mo&gt; &lt;mn&gt;1&lt;/mn&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt; &lt;mo&gt;-&lt;/mo&gt; &lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt; &lt;/msup&gt; &lt;msup&gt;&lt;mi&gt;Δ&lt;/mi&gt; &lt;mi&gt;r&lt;/mi&gt;&lt;/msup&gt; &lt;mo&gt;log&lt;/mo&gt; &lt;mover&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mo&gt;¯&lt;/mo&gt;&lt;/mover&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;n&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/mrow&gt; &lt;/math&gt; than 0. By settling the problem, we are able to show that &lt;dispformula&gt; &lt;math&gt; &lt;mrow&gt; &lt;mtable&gt; &lt;mtr&gt; &lt;mtd&gt; &lt;mrow&gt;&lt;munder&gt;&lt;mo&gt;lim&lt;/mo&gt; &lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt; &lt;mo&gt;→&lt;/mo&gt; &lt;","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"9 1","pages":"9"},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9763134/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10841463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sato-Tate distribution of p-adic hypergeometric functions. p进超几何函数的Sato-Tate分布。
IF 0.6
Research in Number Theory Pub Date : 2023-01-01 Epub Date: 2022-11-29 DOI: 10.1007/s40993-022-00414-w
Sudhir Pujahari, Neelam Saikia
{"title":"Sato-Tate distribution of <i>p</i>-adic hypergeometric functions.","authors":"Sudhir Pujahari, Neelam Saikia","doi":"10.1007/s40993-022-00414-w","DOIUrl":"10.1007/s40993-022-00414-w","url":null,"abstract":"<p><p>Recently Ono, Saad and the second author [21] initiated a study of value distribution of certain families of Gaussian hypergeometric functions over large finite fields. They investigated two families of Gaussian hypergeometric functions and showed that they satisfy semicircular and Batman distributions. Motivated by their results we aim to study distributions of certain families of hypergeometric functions in the <i>p</i>-adic setting over large finite fields. In particular, we consider two and six parameters families of hypergeometric functions in the <i>p</i>-adic setting and obtain that their limiting distributions are semicircular over large finite fields. In the process of doing this we also express the traces of <i>p</i>th Hecke operators acting on the spaces of cusp forms of even weight <math><mrow><mi>k</mi> <mo>≥</mo> <mn>4</mn></mrow> </math> and levels 4 and 8 in terms of <i>p</i>-adic hypergeometric function which is of independent interest. These results can be viewed as <i>p</i>-adic analogous of some trace formulas of [1, 2, 6].</p>","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":" ","pages":"4"},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9708806/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35346191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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