SUMS OF SQUARES FROM ELLIPTIC PFAFFIANS-Reference-Cited by-同舟云学术

SUMS OF SQUARES FROM ELLIPTIC PFAFFIANS

Published:2008-12 Issue:06 Volume:04 Page:873-902
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

ROSENGREN HJALMAR¹

Affiliation:

1. Department of Mathematics, Chalmers University of Technology and Göteborg University, SE-412 96 Göteborg, Sweden

Abstract

We give a new proof of Milne's formulas for the number of representations of an integer as a sum of 4m2 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 2m2 squares.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042108001778

Reference24 articles.

1. RECENT PROGRESS IN THE STUDY OF REPRESENTATIONS OF INTEGERS AS SUMS OF SQUARES

2. Basic Hypergeometric Series

3. Partition Identities and a Theorem of Zagier

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