K. Saito's Conjecture for Nonnegative Eta Products and Analogous Results for Other Infinite Products

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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 [17] and Garvan, Kim and Stanton [10]. A number of other infinite products are shown to have nonnegative coefficients. In the process a new generalization of the quintuple product identity is derived.
15 pages; greatly expanded version of the earlier 8 page paper math.NT/0607606

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Number Theory, Combinatorics, 05A30, 11F20 (Primary); 05A19, 11B65, 11F27, 11F30, 33D15 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/123143

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0702027
 http://arxiv.org/abs/math/0702027

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arXiv