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A note on small gaps between nonzero Fourier coefficients of cusp forms


Authors: Soumya Das and Satadal Ganguly
Journal: Proc. Amer. Math. Soc. 144 (2016), 2301-2305
MSC (2010): Primary 11F30; Secondary 11F11, 11G05
DOI: https://doi.org/10.1090/proc/12887
Published electronically: October 1, 2015
MathSciNet review: 3477047
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Abstract: It is shown that there are infinitely many primitive cusp forms $ f$ of weight $ 2$ with the property that for all $ X$ large enough, every interval $ (X, X+cX^{1/4})$, where $ c>0$ depends only on the form, contains an integer $ n$ such that the $ n$-th Fourier coefficient of $ f$ is nonzero.


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Additional Information

Soumya Das
Affiliation: Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
Email: soumya.u2k@gmail.com

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

DOI: https://doi.org/10.1090/proc/12887
Keywords: Fourier coefficients of cusp forms, elliptic curves, sums of two squares
Received by editor(s): January 25, 2015
Received by editor(s) in revised form: June 29, 2015
Published electronically: October 1, 2015
Communicated by: Kathrin Bringmann
Article copyright: © Copyright 2015 American Mathematical Society