Despite its seemingly deterministic nature, the study of whole numbers, especially prime
numbers, has many interactions with probability theory, the theory of random processes and …

The style of this book is a bit idiosyncratic. The results that interest us belong to number
theory, but the emphasis in the proofs will be on the probabilistic aspects, and on the …

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 …

We consider the distribution of polygonal paths joining the partial sums of normalized
Kloosterman sums modulo an increasingly high power $ p^ n $ of a fixed odd prime $ p $, a …

Let $ p $ be a prime number and $\left (\frac {\cdot}{p}\right) $ be the Legendre symbol
modulo $ p $. The Legendre path attached to $ p $ is the polygonal path whose vertices are …

arXiv:1709.05192v1 [math.NT] 15 Sep 2017 Page 1 ON THE SUPPORT OF THE
KLOOSTERMAN PATHS EMMANUEL KOWALSKI AND WILL SAWIN Abstract. We obtain …

Let be sufficiently small and let. We show that if X is large enough in terms of, then for any
squarefree integer that is-smooth one can obtain an asymptotic formula with power-saving …

We prove that the set of (x 1,…, xd)∈[0, 1) d, such that lim _ N→∞|∑ n= 1 N exp⁡(2 π i (x 1
n+…+ xdnd))|= 0, contains a dense G δ set in [0, 1) d and has a positive Hausdorff …

Kloosterman paths of prime powers moduli Page 1 Kloosterman paths of prime powers
moduli Emmanuel ROYER in collaboration with Guillaume RICOTTA and igor …

Cette thèse traite de certains aspects analytiques liés aux coefficients de Fourier des formes
modulaires de poids demi-entier. On étudie en particulier deux problèmes a priori bien …