Sums of squares from elliptic pfaffians

Details Sums of squares from elliptic pfaffians Sums of squares from elliptic pfaffians

2006-10-09

arxiv.org/abs/math/0610278v1

International Journal of Number Theory 4 (2008), 873-902

Mathematics

Number Theory

30 pages

Scientific paper

We give a new proof of Milne's formulas for the number of representations of
an integer as a sum of 4m^2 and 4m(m+1) squares. The proof is based on explicit
evaluation of pfaffians with elliptic function entries, and relates Milne's
formulas to Schur Q-polynomials and to correlation functions for continuous
dual Hahn polynomials. We also state a new formula for 2m^2 squares.

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