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

Kumar, Narasimha (2016) On the gaps between non-zero Fourier coefficients of cusp forms of higher weight. Ramanujan Journal. pp. 1-14. ISSN 1382-4090 (In Press)

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Abstract

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+cX14) 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 if(n)≪n14 for all n≫0.

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IITH Creators:
IITH CreatorsORCiD
Kumar, NarasimhaUNSPECIFIED
Item Type: Article
Uncontrolled Keywords: Elliptic curves, Rational isogeny,Fourier coefficients of modular forms, 2-adically close, Higher congruence
Subjects: ?? sub3.8 ??
Divisions: Department of Mathematics
Depositing User: Team Library
Date Deposited: 15 Nov 2016 06:25
Last Modified: 15 Nov 2016 06:25
URI: http://raiithold.iith.ac.in/id/eprint/2870
Publisher URL: http://dx.doi.org/10.1007/s11139-016-9837-6
OA policy: http://www.sherpa.ac.uk/romeo/issn/1382-4090/
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