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

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dc.creatorBerkovich, Alexander
dc.creatorGarvan, Frank G.
dc.date2007-02-01
dc.date.accessioned2026-07-07T07:44:17Z
dc.date.available2026-07-07T07:44:17Z
dc.descriptionWe 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.
dc.description15 pages; greatly expanded version of the earlier 8 page paper math.NT/0607606
dc.identifierhttps://arxiv.org/abs/math/0702027
dc.identifierhttp://arxiv.org/abs/math/0702027
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123143
dc.subjectNumber Theory
dc.subjectCombinatorics
dc.subject05A30, 11F20 (Primary); 05A19, 11B65, 11F27, 11F30, 33D15 (Secondary)
dc.titleK. Saito's Conjecture for Nonnegative Eta Products and Analogous Results for Other Infinite Products
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