RICOTTA, Guillaume; ROYER, Emmanuel

doi:10.4171/CMH/442

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RICOTTA, Guillaume
Institut de Mathématiques de Bordeaux [IMB]

ROYER, Emmanuel
Laboratoire de Mathématiques Blaise Pascal [LMBP]

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Commentarii Mathematici Helvetici. 2018-09-10, vol. 93, n° 3, p. 493-532

European Mathematical Society

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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.< Réduire

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Kloosterman paths of prime powers moduli

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