p-adic Properties for Taylor Coefficients of Half-integral Weight Modular Forms on Γ1(4)

被引：0

作者：

Kim, Jigu ^{[1
]}

Lee, Yoonjin ^{[1
,2
]}

机构：

[1] Ewha Womans Univ, Inst Math Sci, Seoul, South Korea

[2] Korea Inst Adv Study, Seoul, South Korea

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2023年 / 27卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

modular forms; Taylor coefficients; congruences; CONGRUENCES;

D O I：

10.11650/tjm/220802

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a prime p 3 (mod 4) and m >= 2, Romik raised a question about whether the Taylor coefficients around root-1 of the classical Jacobi theta function.3 eventually vanish modulo p(m). This question can be extended to a class of modular forms of half-integral weight on Gamma(1)(4) and CM points; in this paper, we prove an affirmative answer to it for primes p >= 5. Our result is also a generalization of the results of Larson and Smith for modular forms of integral weight on SL2(Z).

引用

页码：23 / 38

页数：16

共 18 条

[1]

Berndt B.C., 1985, Ramanujan's Notebooks

[2] PERIODICITIES FOR TAYLOR COEFFICIENTS OF HALF-INTEGRAL WEIGHT MODULAR FORMS [J].