The Ramanujan Journal最新文献_第3页

Modular forms with non-vanishing central values and linear independence of Fourier coefficients 中心值不求和傅立叶系数线性独立的模块形式

The Ramanujan Journal Pub Date : 2024-08-19 DOI: 10.1007/s11139-024-00931-5

Debargha Banerjee, Priyanka Majumder

引用次数: 0

On Fourier coefficients associated to automorphic L-functions over a binary quadratic form and its applications 关于与二元二次型上的自定 L 函数相关的傅里叶系数及其应用

The Ramanujan Journal Pub Date : 2024-08-17 DOI: 10.1007/s11139-024-00916-4

Guodong Hua

{"title":"On Fourier coefficients associated to automorphic L-functions over a binary quadratic form and its applications","authors":"Guodong Hua","doi":"10.1007/s11139-024-00916-4","DOIUrl":"https://doi.org/10.1007/s11139-024-00916-4","url":null,"abstract":"Let f and g be two distinct normalized primitive Hecke cusp forms of even integral weights (k_{1}) and (k_{2}) for the full modular group (Gamma =SL(2,{mathbb {Z}})), respectively. Denote by (lambda _{fotimes fotimes fotimes g}(n)) and (lambda _{text {sym}^{2}fotimes fotimes g}(n)) the nth normalized coefficients of the automorphic L-functions (L(fotimes fotimes fotimes g,s)) and (L(text {sym}^{2}fotimes fotimes g,s)), respectively. In this paper, we are interested in the average behavior of the coefficients (lambda _{fotimes fotimes fotimes g}(n)) and (lambda _{text {sym}^{2}fotimes fotimes g}(n)) on a primitive integral binary quadratic form with negative discriminant whose class number is 1, and we also provide the asymptotic formulae of these summatory functions. As an application, we also consider the number of sign changes of the sequences ({lambda _{fotimes fotimes fotimes g}(n)}_{ngeqslant 1}) and ({lambda _{text {sym}^{2}fotimes fotimes g}(n)}_{ngeqslant 1}) on the same binary quadratic form in short intervals.","PeriodicalId":501430,"journal":{"name":"The Ramanujan Journal","volume":"94 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177703","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

C-polynomials and LC-functions: towards a generalization of the Hurwitz zeta function C-polynomials and LC-functions: toward a generalization of the Hurwitz zeta function（C-多项式和 LC 函数：实现赫维茨泽塔函数的一般化

The Ramanujan Journal Pub Date : 2024-08-16 DOI: 10.1007/s11139-024-00919-1

Lahcen Lamgouni

{"title":"C-polynomials and LC-functions: towards a generalization of the Hurwitz zeta function","authors":"Lahcen Lamgouni","doi":"10.1007/s11139-024-00919-1","DOIUrl":"https://doi.org/10.1007/s11139-024-00919-1","url":null,"abstract":"Let (f(t)=sum _{n=0}^{+infty }frac{C_{f,n}}{n!}t^n) be an analytic function at 0, and let (C_{f, n}(x)=sum _{k=0}^{n}left( {begin{array}{c}n kend{array}}right) C_{f,k} x^{n-k}) be the sequence of Appell polynomials, referred to as C-polynomials associated to f, constructed from the sequence of coefficients (C_{f,n}). We also define (P_{f,n}(x)) as the sequence of C-polynomials associated to the function (p_{f}(t)=f(t)(e^t-1)/t), called P-polynomials associated to f. This work investigates three main topics. Firstly, we examine the properties of C-polynomials and P-polynomials and the underlying features that connect them. Secondly, drawing inspiration from the definition of P-polynomials and subject to an additional condition on f, we introduce and study the bivariate complex function (P_{f}(s,z)=sum _{k=0}^{+infty }left( {begin{array}{c}z kend{array}}right) P_{f,k}s^{z-k}), which generalizes the (s^z) function and is denoted by (s^{(z,f)}). Thirdly, the paper’s main contribution is the generalization of the Hurwitz zeta function and its fundamental properties, most notably Hurwitz’s formula, by constructing a novel class of functions defined by (L(z,f)=sum _{n=n_{f}}^{+infty }n^{(-z,f)}), which are intrinsically linked to C-polynomials and referred to as LC-functions associated to f (the constant (n_{f}) is a positive integer dependent on the choice of f).","PeriodicalId":501430,"journal":{"name":"The Ramanujan Journal","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177704","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

Points of bounded height on weighted projective spaces over global function fields 全局函数域上加权投影空间上的有界高点

The Ramanujan Journal Pub Date : 2024-08-15 DOI: 10.1007/s11139-024-00892-9

Tristan Phillips

引用次数: 0

A generalization of Siegel’s method to Jacobi’s $$vartheta _1$$ function 西格尔方法对雅各比$$vartheta _1$$函数的推广

The Ramanujan Journal Pub Date : 2024-08-11 DOI: 10.1007/s11139-024-00894-7

Maher Mamah, Ali Saraeb

引用次数: 0

Asymptotics of reciprocal supernorm partition statistics 倒数超模分区统计的渐近性

The Ramanujan Journal Pub Date : 2024-08-10 DOI: 10.1007/s11139-024-00893-8

Jeffrey C. Lagarias, Chenyang Sun