RICOTTA, Guillaume; ROYER, Emmanuel; SHPARLINSKI, Igor

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RICOTTA, Guillaume
Institut de Mathématiques de Bordeaux [IMB]

ROYER, Emmanuel
Laboratoire de Mathématiques Blaise Pascal [LMBP]

SHPARLINSKI, Igor
School of Mathematics and statistics [Sydney]

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Article de revue

Ce document a été publié dans

Bulletin de la société mathématique de France. 2020, vol. 148, n° 1, p. 173-188

Société Mathématique de France

Date de soutenance

2020

Résumé en anglais

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.< Réduire

Mots clés en anglais

Kloosterman sums

moments

probability in Banach spaces

URI

https://oskar-bordeaux.fr/handle/20.500.12278/192576

Project ANR

Familles de fonctions L: analyse, interactions, résultats effectifs - ANR-17-CE40-0012

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251