Congruences for Fourier coefficients of eta‐quotients modulo powers of 5, 7, 11, 13, and 17

Abstract

In this paper, we investigate the Fourier coefficients of the eta‐quotients of the forms where is the Dedekind eta function, , and 17; is a positive integer, and are arbitrary integers. We prove Ramanujan's type congruences for the Fourier coefficients of modulo powers of prime . We recover several results due to Atkin, Garvan, Gordon, Wang, Mestrige, and others. We give few examples, and we establish an improvement for Wang's results related to the 11‐regular partition function.