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)
|
Text
1602.05745v2.pdf - Accepted Version Download (207kB) | Preview |
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.
| IITH Creators: |
|
||||
|---|---|---|---|---|---|
| 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/ | ||||
| Related URLs: |
Actions (login required)
 |
View Item |
|
Statistics for this ePrint Item |
Altmetric
Altmetric
Altmetric