Kloosterman paths of prime powers moduli, II
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | RICOTTA, Guillaume | |
| hal.structure.identifier | Laboratoire de Mathématiques Blaise Pascal [LMBP] | |
| dc.contributor.author | ROYER, Emmanuel | |
| hal.structure.identifier | School of Mathematics and statistics [Sydney] | |
| dc.contributor.author | SHPARLINSKI, Igor | |
| dc.date | 2020 | |
| dc.date.accessioned | 2024-04-04T02:57:34Z | |
| dc.date.available | 2024-04-04T02:57:34Z | |
| dc.date.issued | 2020 | |
| dc.identifier.issn | 0037-9484 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192576 | |
| dc.description.abstractEn | G. Ricotta and E. Royer (2018) have recently proved that the polygonal paths joining the partial sums of the normalized classical Kloosterman sums $S(a,b;p^n)/p^(n/2) converge in law in the Banach space of complex-valued continuous function on [0,1] to an explicit random Fourier series as (a,b) varies over (Z/p^nZ)^\times\times(Z/p^nZ)^\times, p tends to infinity among the odd prime numbers and n>=2 is a fixed integer. This is the analogue of the result obtained by E. Kowalski and W. Sawin (2016) in the prime moduli case. The purpose of this work is to prove a convergence law in this Banach space as only a varies over (Z/p^nZ)^\times, p tends to infinity among the odd prime numbers and n>=31 is a fixed integer. | |
| dc.description.sponsorship | Familles de fonctions L: analyse, interactions, résultats effectifs - ANR-17-CE40-0012 | |
| dc.language.iso | en | |
| dc.publisher | Société Mathématique de France | |
| dc.subject.en | Kloosterman sums | |
| dc.subject.en | moments | |
| dc.subject.en | probability in Banach spaces | |
| dc.title.en | Kloosterman paths of prime powers moduli, II | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.subject.hal | Mathématiques [math]/Anneaux et algèbres [math.RA] | |
| dc.identifier.arxiv | 1810.01150 | |
| bordeaux.journal | Bulletin de la société mathématique de France | |
| bordeaux.page | 173-188 | |
| bordeaux.volume | 148 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02455246 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02455246v1 | |
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