Sommes de modules de sommes d’exponentielles

Etienne Fouvry and Philippe Michel

Vol. 209 (2003), No. 2, 261–288

DOI: 10.2140/pjm.2003.209.261

Abstract

Let Kl(a,b;n) be the usual Kloosterman sum modulo n, with coefficients a and b. We give upper and lower bounds for the sum ∑ _n≤x|Kl(1,1;n)|∕, and for related sums, by using large sieve techniques and Deligne-Katz theory of exponential sums. Extensions to more general exponential sums of dimension one are also given.

Milestones

Received: 4 February 2002

Published: 1 April 2003

Correction: 1 May 2006