Vanishing coefficients in quotients of theta functions with odd moduli

被引：0
|
作者：
Du, Julia Q. D. [1 ]
Tang, Dazhao [2 ]
机构：
[1] Hebei Normal Univ, Sch Math Sci, Postdoctoral Res Stn Math, Shijiazhuang 050024, Peoples R China
[2] Chongqing Normal Univ, Sch Math Sci, Chongqing 401331, Peoples R China
来源：
INTERNATIONAL JOURNAL OF NUMBER THEORY | 2023年
基金：
中国国家自然科学基金;
关键词：
Vanishing coefficients; theta functions; arithmetic progressions; modular forms; CONTINUED-FRACTION; INFINITE; EXPANSION;
D O I：
10.1142/S179304212350121
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Following recent studies of vanishing coefficients in arithmetic progressions in infinite q-series products, we further prove that such phenomenon also exists in a family of quotients of theta functions with odd moduli. Moreover, we find that some arithmetic progressions with vanishing coefficients could be shared by an infinite family of quotients of theta functions. Finally, we present several related conjectures that merit further investigation.
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页数：31
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