More congruences for the coefficients of quotients of Eisenstein series Original Research Article

Berndt and Yee (Acta Arith. 104 (2002) 297) recently proved congruences for the coefficients of certain quotients of Eisenstein series. In each case, they showed that an arithmetic progression of coefficients is identically zero modulo a small power of 3 or 7. The present paper extends these results by proving that there are infinite classes of odd primes for which the set of coefficients that are zero modulo an arbitrary prime power is a set of arithmetic density one. A new family of explicit congruences modulo arbitrary powers of 2 is also found.