K. Saito's Conjecture for Nonnegative Eta Products
Number Theory
2007-05-23 v1 Combinatorics
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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Cite
@article{arxiv.math/0607606,
title = {K. Saito's Conjecture for Nonnegative Eta Products},
author = {Alexander Berkovich and Frank G. Garvan},
journal= {arXiv preprint arXiv:math/0607606},
year = {2007}
}
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8 pages