Kloosterman paths of prime powers moduli
| 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 | |
| dc.date.accessioned | 2024-04-04T03:04:18Z | |
| dc.date.available | 2024-04-04T03:04:18Z | |
| dc.date.issued | 2018-09-10 | |
| dc.identifier.issn | 0010-2571 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193140 | |
| dc.description.abstractEn | Emmanuel Kowalski and William Sawin proved, using a deep independence result of Kloosterman sheaves, that the polygonal paths joining the partial sums of the normalized classical Kloosterman sums S(a,b0;p)/p^{1/2} converge in the sense of finite distributions to a specific random Fourier series, as a varies over (Z/pZ)^*, b0 is fixed in (Z/pz)* and p tends to infinity among the odd prime numbers. This article considers the case of S(a,b0;p^n)/p^{n/2}, as a varies over (Z/p^nZ)^*, b0 is fixed in (Z/p^nZ)^*, p tends to infinity among the odd prime numbers and n>=2 is a fixed integer. A convergence in law in the Banach space of complex-valued continuous function on [0,1] is also established, as (a,b) varies over (Z/p^nZ)*.(Z/p^nZ)*, 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 Emmanuel Kowalski and William Sawin in the prime moduli case. | |
| dc.language.iso | en | |
| dc.publisher | European Mathematical Society | |
| dc.title.en | Kloosterman paths of prime powers moduli | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.4171/CMH/442 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.subject.hal | Mathématiques [math]/Anneaux et algèbres [math.RA] | |
| dc.identifier.arxiv | 1609.03694 | |
| bordeaux.journal | Commentarii Mathematici Helvetici | |
| bordeaux.page | 493-532 | |
| bordeaux.volume | 93 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 3 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01917568 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01917568v1 | |
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