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.
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页码：95 / 109
页数：15
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