Sur le changement de signe des sommes de Kloosterman

Abstract

Combining sieve methods with automorphic form theory and techniques from $\ell$-adic cohomology, we prove that the sign of Kloosterman sums ${\mathrm{Kl}}(1,1;n)$ changes infinitely often as $n$ ranges over the squarefree integers having all their prime factors larger than $n^{1/23.9}$.