On the counting function of sets with even partition functions

Fethi Ben Said (1) , Jean-Louis Nicolas (2)

1 UM - Université de Monastir - University of Monastir
2 ICJ - Institut Camille Jordan

Let q be an odd positive integer and P 2 F2[z] be of order q and such that P(0) = 1. We denote by A = A(P) the unique set of positive integers satisfying P1 n=0 p(A; n)zn P(z) (mod 2), where p(A; n) is the number of partitions of n with parts in A. In [5], it is proved that if A(P; x) is the counting function of the set A(P) then A(P; x) x(log x)

Domaines: Théorie des nombres [math.NT]

Fethi Ben Said, Jean-Louis Nicolas. On the counting function of sets with even partition functions. 2011. ⟨hal-00558991v1⟩