A note on the extended Bruinier-Kohnen conjecture

Let \(f\) be a cuspform of integral half-weight \(k+1/2\), whose Fourier coefficients \(a(n)\) not necessarily real. We verify partially an extension of a conjecture of Bruinier and Kohnen on the equi-distribution of the signs of \(a(n)\) (when are real), conjectured by the first author in \cite{Amr...

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Published in:arXiv.org 2018-11
Main Authors: Mohammed Amin Amri, Ziane, M'hammed
Format: Article
Language:English
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Summary:Let \(f\) be a cuspform of integral half-weight \(k+1/2\), whose Fourier coefficients \(a(n)\) not necessarily real. We verify partially an extension of a conjecture of Bruinier and Kohnen on the equi-distribution of the signs of \(a(n)\) (when are real), conjectured by the first author in \cite{Amri2} for the sequence \(\{a(tp^{2\nu})\}_{p,\text{prime}}\), where \(\nu\) an odd positive integer and \(t\) a square-free integer.
ISSN:2331-8422
DOI:10.48550/arxiv.1711.02431