Dominant residue classes concerning the summands of partitions

Cécile Dartyge (1) , Mihaly Szalay (2)

1 IECN - Institut Élie Cartan de Nancy
2 Alfred Renyi Mathematical Institute

Let 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.

Mots clés: partitions; classes de congruence

Domaines: Théorie des nombres [math.NT]

Cécile Dartyge, Mihaly Szalay. Dominant residue classes concerning the summands of partitions. Functiones et Approximatio Commentarii Mathematici, 2007. ⟨hal-00143686⟩