On the number of primitive representations of integers as sums of squares |
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| Authors: | Shaun Cooper Michael Hirschhorn |
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| Institution: | (1) Institute of Information and Mathematical Sciences, Massey University, Private Bag 102904, North Shore Mail Centre, Auckland, New Zealand;(2) School of Mathematics, University of New South Wales, Sydney, 2052, Australia |
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| Abstract: | Formulas for the number of primitive representations of any integer n as a sum of k squares are given, for 2 ≤ k ≤ 8, and for certain values of n, for 9 ≤ k ≤ 12. The formulas have a similar structure and are striking for their simplicity.
Dedicated to Richard Askey on the occasion of his 70th birthday.
2000 Mathematics Subject Classification Primary—11E25; Secondary—05A15, 33E05. |
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| Keywords: | Sum of squares M?bius inversion Generating function Divisor sum |
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