On the gaps between non-zero Fourier coefficients of cusp forms of higher weight

被引：3

作者：

Kumar, Narasimha ^{[1
]}

机构：

[1] Indian Inst Technol Hyderabad, Dept Math, Kandi 502285, Sangareddy, India

来源：

RAMANUJAN JOURNAL | 2018年 / 45卷 / 01期

关键词：

Elliptic curves; Rational isogeny; Fourier coefficients of modular forms; 2-adically close; Higher congruence; B-FREE NUMBERS; SHORT INTERVALS; MODULAR-FORMS; EXPANSION; PROGRESSIONS;

D O I：

10.1007/s11139-016-9837-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that if a modular cuspidal eigenform f of weight 2k is 2-adically close to an elliptic curve E/Q, which has a cyclic rational 4-isogeny, then n-th Fourier coefficient of f is non-zero in the short interval (X, X + cX(1/4)) for all X >> 0 and for some c > 0. We use this fact to produce non-CM cuspidal eigenforms f of level N > 1 and weight k > 2 such that i(f)(n) << n(1/4) for all n >> 0.

引用

页码：95 / 109

页数：15

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