Identical Vanishing of Coefficients in the Series Expansion of Eta Quotients, modulo 4, 9 and 25

Tim Huber, James McLaughlin, Dongxi Ye

Let $A(q)={\sum }_{n=0}^{\infty }{a}_n{q}^n$ and $B(q)={\sum }_{n=0}^{\infty }{b}_n{q}^n$ be two eta quotients. Previously, we considered the problem of when \[ a_n=0 <=> b_n=0. \] Here we consi…