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