On the gaps between nonzero Fourier coefficients of eigenforms with CM-Reference-Cited by-同舟云学术

On the gaps between nonzero Fourier coefficients of eigenforms with CM

Published:2017-11-21 Issue:01 Volume:14 Page:95-101
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Kaushik Surjeet¹,Kumar Narasimha¹

Affiliation:

1. Department of Mathematics, Indian Institute of Technology Hyderabad, Kandi, Sangareddy, 502285, India

Abstract

Suppose [Formula: see text] is an elliptic curve over [Formula: see text] of conductor [Formula: see text] with complex multiplication (CM) by [Formula: see text], and [Formula: see text] is the corresponding cuspidal Hecke eigenform in [Formula: see text]. Then [Formula: see text]th Fourier coefficient of [Formula: see text] is nonzero in the short interval [Formula: see text] for all [Formula: see text] and for some [Formula: see text]. As a consequence, we produce infinitely many cuspidal CM eigenforms [Formula: see text] level [Formula: see text] and weight [Formula: see text] for which [Formula: see text] holds, for all [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042118500070

Reference17 articles.

1. Nonvanishing of Fourier coefficients of modular forms

2. On the Sizes of Gaps in the Fourier Expansion of Modular Forms

3. Nonvanishing of Fourier coefficients of newforms in progressions

4. B-free numbers in short arithmetic progressions

5. NONVANISHING OF THE RAMANUJAN TAU FUNCTION IN SHORT INTERVALS

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