Positivity of Eta Products—a Certain Case of K. Saito’s Conjecture

Abstract

We prove that for any prime p, the Fourier coeffcients of η(_p_τ)p/η(τ) are all non-negative, where η(τ) is the Dedekind eta function. This is a proof of some parts of K. Saito’s conjecture on such positivity of eta products associated with regular systems of weight.