hal.structure.identifier	Institut de Mathématiques de Bordeaux [IMB]
dc.contributor.author	DARREYE, Corentin
dc.date.accessioned	2024-04-04T02:49:04Z
dc.date.available	2024-04-04T02:49:04Z
dc.identifier.uri	https://oskar-bordeaux.fr/handle/20.500.12278/191791
dc.description.abstractEn	Let $f$ be a half-integral weight cusp form of level $4N$ for odd and squarefree $N$ and let $a(n)$ denote its $n^{\rm th}$ normalized Fourier coefficient. Assuming that all the coefficients $a(n)$ are real, we study the sign of $a(n)$ when $n$ runs through an arithmetic progression. As a consequence, we establish a lower bound for the number of integers $n\le x$ such that $a(n)>n^{-\alpha}$ where $x$ and $\alpha$ are positive and $f$ is not necessarily a Hecke eigenform.
dc.language.iso	en
dc.title.en	Sign of Fourier coefficients of half-integral weight modular forms in arithmetic progressions
dc.type	Document de travail - Pré-publication
dc.subject.hal	Mathématiques [math]
dc.identifier.arxiv	2007.06224
bordeaux.hal.laboratories	Institut de Mathématiques de Bordeaux (IMB) - UMR 5251	*
bordeaux.institution	Université de Bordeaux
bordeaux.institution	Bordeaux INP
bordeaux.institution	CNRS
hal.identifier	hal-02976193
hal.version	1
hal.origin.link	https://hal.archives-ouvertes.fr//hal-02976193v1
bordeaux.COinS	ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=DARREYE,%20Corentin&rft.genre=preprint

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Sign of Fourier coefficients of half-integral weight modular forms in arithmetic progressions