[Abstract] Alexander Berkovich and Frank G. Garvan; K. Saito's Conjecture for Nonnegative Eta Products and Analogous Results for Other Infinite Products


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 [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.

PREVIOUS VERSION

The url of this page is http://www.math.ufl.edu/~frank/abstracts/saito.html.
Created by F.G. Garvan (fgarvan@ufl.edu) on Thursday, March 01, 2007.
Last update made Thu Mar 1 23:02:27 EST 2007.

MAIL fgarvan@ufl.edu