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arXiv · 2211.12985

The first negative Fourier coefficient of an Eisenstein series newform

Sebastián Carrillo Santana
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Abstract

There have been a number of papers on statistical questions concerning the sign changes of Fourier coefficients of newforms. In one such paper, Linowitz and Thompson gave a conjecture describing when, on average, the first negative sign of the Fourier coefficients of an Eisenstein series newform occurs. In this paper, we correct their conjecture and prove the corrected version.

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Sebastián Carrillo Santana. 2022-11-23. The first negative Fourier coefficient of an Eisenstein series newform. https://arxiv.org/abs/2211.12985

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