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math.NT2008
On the representations of integers by the sextenary quadratic form x^2+y^2+z^2+ 7s^2+7t^2+ 7u^2 and 7-cores
Alexander Berkovich, Hamza Yesilyurt
In this paper we derive an explicit formula for the number of representations of an integer by the sextenary form x^2+y^2+z^2+ 7s^2+7t^2+ 7u^2. We establish the following intriguin…
math.NT2008★ 1 cited
The tri-pentagonal number theorem and related identities
Alexander Berkovich
I revisit an automated proof of Andrews' pentagonal number theorem found by Riese. I uncover a simple polynomial identity hidden behind his proof. I explain how to use this identit…
math.NT2007
K. Saito's Conjecture for Nonnegative Eta Products and Analogous Results for Other Infinite Products
Alexander Berkovich, Frank G. Garvan
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 func…