# 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 $n^{1/23.9}$.

## Authors

Étienne Fouvry

Mathématiques Bât, Univ. Paris-Sud, Campus d'Orsay, F-91405 Orsay Cedex, France

Philippe Michel

Département de Mathématiques, Univ. Montpelier II, Place E. Bataillon, FR-34095 Montpellier Cedex, France