On the counting function of sets with even partition functions

Mathematics – Number Theory

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Scientific paper

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)

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