PARITY OF FOURIER COEFFICIENTS OF MODULAR FORMS

摘要

A partition of a non-negative integer n is a non-increasing sequence of positive integers whose sum is n. It is of interest to examine the number of partitions of n under some additional restriction on the summands. Various partition functions arise in the representation theory of permutation groups (see [2]). For example, if p is prime, then let b_p(n) denote the number of partitions of a non-negative integer n where the summands are not multiples of p. If n is a positive integer, then b_p(n) denotes the number of irreducible representations of the symmetric group S_n over the finite field with p elements [2, Lemma 6.1.2].