arXiv Open Access 2007

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

Alexander Berkovich Frank G. Garvan

Lihat Sumber

Abstrak

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.

Topik & Kata Kunci

math.NT math.CO

Penulis (2)

Alexander Berkovich

Frank G. Garvan

Format Sitasi

APA MLA BibTeX

Berkovich, A., Garvan, F.G. (2007). K. Saito's Conjecture for Nonnegative Eta Products and Analogous Results for Other Infinite Products. https://arxiv.org/abs/math/0702027

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2007
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓