Dominant residue classes concerning the summands of partitions

26 pages, accepté pour publication dans le journal Functiones et approximatioInternational audienceLet n and d be positive integers satisfying d< n^{1/8-h} with h arbitrarly small. Let N_1, ...,N_d be some integers. We obtain for a large range in N_1,...,N_d, an asymptotic formula of the number of partitions of with N_1 parts congruent to 1 modulo d,N_2 parts congruent to 2 modulo d,....,N_d parts modulo d. Next we derive many results on the distribution of the parts of the partitions in residue classes