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On representations of a number as a sum of three squares

Authors
  • Hirschborn, Michael D.
  • Sellers, James A.
Type
Published Article
Journal
Discrete Mathematics
Publication Date
Jan 01, 1999
Accepted Date
Jun 08, 1998
Volume
199
Issue
1-3
Pages
85–101
Identifiers
DOI: 10.1016/S0012-365X(98)00288-X
Source
Elsevier
Keywords
License
Unknown

Abstract

We give a variety of results involving s(n), the number of representation of n as a sum of three squares. Using elementary techniques we prove that if 9 †n, via the theory of modular forms of half integer weight we prove the corresponding result with 3 replaced by p, an odd prime. This leads to a formula for s(n) in terms of s(n′), where n′ is the square-free part of n.We also find generating function formulae for various subsequences of {s(n)}, for instance

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