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The thesis gave a fine study on the distribution of the coefficients ofautomorphic L-functions for GL(m) with m>1. In particular we have treated twotypes of problems: change of signs of these coefficients (when they are real)and their decompensation on the prime numbers. Chapter 2 is devoted to theresults known concerning the first problem in the case of classical modularforms and to explain our motivation of research. In Chapter 3, we treated thecase of primitive Maass forms and obtained an estimate of the subconvexity-typefor the least integer n such that the n-th coefficient is negative. Chapter 4is the main part of the thesis. For the coefficients of the L-functionassociated with an irreducible unitary cuspidal representation for GL(m) withm>1, we established an elegant inequality of Hecke type, which shows that thesecoefficients on the first m powers of an arbitrary unramified prime numbercannot be small simultaneously. As an application, we obtained a polynomialtype estimate for the least integer n such that the n-th coefficient isnegative. In Chapters 5 and 6, we studied the long and short summations ofcoefficients of L-functions for GL(m) on the prime numbers to test theirdecompensation, respectively. In particular we gave a perfect generalization ofSelberg's normal density theorem when m>1.

Linnik-type problems for automorphic L-functions; Problemes de type Linnik pour les fonctions L de formes automorphes