Kloosterman paths of prime powers moduli, II
Language
en
Article de revue
This item was published in
Bulletin de la société mathématique de France. 2020, vol. 148, n° 1, p. 173-188
Société Mathématique de France
Date
2020English Abstract
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 ...Read more >
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.Read less <
English Keywords
Kloosterman sums
moments
probability in Banach spaces
ANR Project
Familles de fonctions L: analyse, interactions, résultats effectifs - ANR-17-CE40-0012
Origin
Hal imported