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Gaps between nonzero Fourier coefficients of cusp forms


Authors: Soumya Das and Satadal Ganguly
Journal: Proc. Amer. Math. Soc. 142 (2014), 3747-3755
MSC (2010): Primary 11F30; Secondary 11F11, 11N25
Published electronically: July 24, 2014
MathSciNet review: 3251716
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Abstract: We prove that for any even integer $ k \geq 12$, there are positive constants $ c$ and $ X_0$ that depend only on $ k$ such that for all nonzero cusp forms $ f$ of weight $ k$ for the full modular group, any interval $ (X, X+c X^{1/4})$ with $ X>X_0$ must contain an integer $ n$ with the $ n$-th Fourier coefficient of $ f$ nonzero.


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Additional Information

Soumya Das
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai – 400005, India
Email: somu@math.tifr.res.in, soumya.u2k@gmail.com

Satadal Ganguly
Affiliation: Indian Statistical Institute, Theoretical Statistics and Mathematics Unit, 203 Barrackpore Trunk Road, Kolkata 700108, India
Email: sgisical@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2014-12164-2
Keywords: Fourier coefficients of cusp forms, sums of two squares
Received by editor(s): August 13, 2012
Received by editor(s) in revised form: December 19, 2012
Published electronically: July 24, 2014
Communicated by: Kathrin Bringmann
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.