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Sums of squares of binomial coefficients, with applications to Picard-Fuchs equations | | H. A. Verrill
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19 Jul 2004 | | Subject: | Combinatorics; Algebraic Geometry MSC-class: 05A10, 14D05 | math.CO math.AG | | Abstract: | For a fixed integer N, and fixed numbers b_1,...,b_N, we consider sequences, the nth term (a_n) of which is the sum of the squares of the terms in the expansion of (b_1 + ... + b_N)^n. In the case all b_i=1, we give a formula for a recurrence relation for the a_n. Otherwise we give an algorithm for finding a recurrence relation. As an application, we give the Picard-Fuchs equations for certain families of elliptic curves. | | Source: | arXiv, math.CO/0407327 | | Services: | Forum | Review | PDF | Favorites | |
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