一些与仿theta函数相关的函数  

Some functions related to some mock theta functions

作　　者：曲帅龙 QU Shuailong(School of Mathematics and Statistics,Qinghai Normal University,810008,Xining,Qinghai,PRC)

机构地区：[1]青海师范大学数学与统计学院,青海省西宁市810008

出　　处：《曲阜师范大学学报(自然科学版)》2025年第2期33-40,共8页Journal of Qufu Normal University(Natural Science)

基　　金：国家自然科学基金(12001309).

摘　　要：在Ramanujan写给Hardy的最后一封信中,引入了17个经典仿theta函数,这些函数可以用欧拉形式、Hecke类型双重求和、Appell-Lerch求和以及亚纯Jocobi形式的傅里叶系数来表示.该文发现了与某些仿theta函数相关的4个新函数.同时构建了这些新函数的Hecke类型双重求和.最后建立了这些函数与一些经典仿theta函数之间的关系.In the last letter to Hardy,Ramanujan introduced 17 classical mock theta functions,which can be represented by Euler forms,Hecke-type double sums,Appell-Lerch sums,and Fourier coefficients of meromorphic Jacobi forms.In this paper,we find four new functions related to some mock theta functions.Meanwhile,we present the Hecke-type double sums for our functions.Lastly,some relations between our new functions and some classical mock theta functions are established.

关 键 词：仿theta函数 Hecke型双重求和 Appell-Lerch求和 

分 类 号：O156.3[理学—数学]