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We prove that for any prime p, the Fourier coefficients of η(pτ ) p /η(τ )a re 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.

Positivity of eta products---a certain case of K. Saito's conjecture