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K. Saito's Conjecture for Nonnegative Eta Products

Alexander Berkovich·Frank G. Garvan
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Abstract

We prove that the Fourier coefficients of a certain general eta product considered by K. Saito are nonnegative. The proof is elementary and depends on a multidimensional theta function identity. The z = 1 case is an identity for the generating function for p-cores due to Klyachko [12] and Garvan, Kim and Stanton [7].

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Alexander Berkovich, Frank G. Garvan. 2006-07-25. K. Saito's Conjecture for Nonnegative Eta Products. https://arxiv.org/abs/math/0607606

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