Sums of squares from elliptic pfaffians
Journal article, 2008

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.


Hjalmar Rosengren

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

International Journal of Number Theory

Vol. 4 873-902

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