Distribution of short sums of classical Kloosterman sums of prime powers moduli
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | RICOTTA, Guillaume | |
| dc.date | 2020 | |
| dc.date.accessioned | 2024-04-04T02:57:19Z | |
| dc.date.available | 2024-04-04T02:57:19Z | |
| dc.date.issued | 2020 | |
| dc.identifier.issn | 1259-1734 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192555 | |
| dc.description.abstractEn | Corentin Perret-Gentil proved, under some very general conditions, that short sums of $\ell$-adic trace functions over finite fields of varying center converges in law to a Gaussian random variable or vector. The main inputs are P.~Deligne's equidistribution theorem, N.~Katz' works and the results surveyed in \cite{MR3338119}. In particular, this applies to $2$-dimensional Kloosterman sums $\mathsf{Kl}_{2,\mathbb{F}_q}$ studied by N.~Katz in \cite{MR955052} and in \cite{MR1081536} when the field $\mathbb{F}_q$ gets large. \par This article considers the case of short sums of normalized classical Kloosterman sums of prime powers moduli $\mathsf{Kl}_{p^n}$, as $p$ tends to infinity among the prime numbers and $n\geq 2$ is a fixed integer. A convergence in law towards a real-valued standard Gaussian random variable is proved under some very natural conditions. | |
| dc.language.iso | en | |
| dc.publisher | Université Blaise-Pascal - Clermont-Ferrand | |
| dc.title.en | Distribution of short sums of classical Kloosterman sums of prime powers moduli | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 1907.01834 | |
| bordeaux.journal | Annales Mathématiques Blaise Pascal | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02476621 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02476621v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Annales%20Math%C3%A9matiques%20Blaise%20Pascal&rft.date=2020&rft.eissn=1259-1734&rft.issn=1259-1734&rft.au=RICOTTA,%20Guillaume&rft.genre=article |
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