K. Saito's Conjecture for Nonnegative Eta Products

Details K. Saito's Conjecture for Nonnegative Eta Products K. Saito's Conjecture for Nonnegative Eta Products

2006-07-25

arxiv.org/abs/math/0607606v1

Mathematics

Number Theory

8 pages

Scientific paper

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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