Kloosterman paths of prime powers moduli

  • Guillaume Ricotta

    Université de Bordeaux I, Talence, France
  • Emmanuel Royer

    Université Clermont Auvergne, Aubière, France

Abstract

In [12], the authors proved, using a deep independence result of Kloosterman sheaves, that the polygonal paths joining the partial sums of the normalized classical Kloosterman sums converge in the sense of finite distributions to a specific random Fourier series, as varies over , is fixed in and tends to infinity among the odd prime numbers. This article considers the case of , as varies over , is fixed in , tends to infinity among the odd prime numbers and is a fixed integer. A convergence in law in the Banach space of complex-valued continuous function on is also established, as varies over , tends to infinity among the odd prime numbers and is a fixed integer. This is the analogue of the result obtained in [12] in the prime moduli case.

Cite this article

Guillaume Ricotta, Emmanuel Royer, Kloosterman paths of prime powers moduli. Comment. Math. Helv. 93 (2018), no. 3, pp. 493–532

DOI 10.4171/CMH/442