Kloosterman paths of prime powers moduli, II

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 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.
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Contributor : Emmanuel Royer <>
Submitted on : Saturday, January 25, 2020 - 5:47:48 PM
Last modification on : Wednesday, February 19, 2020 - 1:10:04 PM

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Guillaume Ricotta, Emmanuel Royer, Igor Shparlinski. Kloosterman paths of prime powers moduli, II. Bulletin de la société mathématique de France, Société Mathématique de France, In press, ⟨10.01150⟩. ⟨hal-02455246⟩

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