RICOTTA, Guillaume; ROYER, Emmanuel; SHPARLINSKI, Igor

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Licencia de uso del documento

RICOTTA, Guillaume
Institut de Mathématiques de Bordeaux [IMB]

ROYER, Emmanuel
Laboratoire de Mathématiques Blaise Pascal [LMBP]

SHPARLINSKI, Igor
School of Mathematics and statistics [Sydney]

Idioma

Article de revue

Este ítem está publicado en

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

Société Mathématique de France

Fecha de defensa

2020

Resumen en inglés

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.< Leer menos

Palabras clave en inglés

Kloosterman sums

moments

probability in Banach spaces

URI

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

Proyecto ANR

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

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251