title: A study in sums of products.
abstract: We give a general version of cancellation in exponential sums that arise as sums of products of trace functions satisfying a suitable independence condition related to the Goursat-Kolchin-Ribet criterion, in a form that is easily applicable in analytic number theory.
authors: Université Paris Sud, Laboratoire de Mathématique, Campus d'Orsay, 91405 Orsay Cedex, France.
authors: Étienne
authors: É
authors: Fouvry
authors: ETH Zürich - D-MATH, Rämistrasse 101, 8092 Zürich, Switzerland kowalski@math.ethz.ch.
authors: Emmanuel
authors: E
authors: Kowalski
authors: EPFL/SB/IMB/TAN, Station 8, 1015 Lausanne, Switzerland.
authors: Philippe
authors: P
authors: Michel
keywords: Riemann hypothesis over finite fields; exponential sums; monodromy; trace functions; ℓ-adic sheaves