Gaps between nonzero Fourier coefficients of cusp forms

Das, Soumya; Ganguly, Satadal

doi:10.1090/S0002-9939-2014-12164-2

Gaps between nonzero Fourier coefficients of cusp forms
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by Soumya Das and Satadal Ganguly PDF

Proc. Amer. Math. Soc. 142 (2014), 3747-3755 Request permission

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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