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On the sum of a square and a square of a prime
Published online by Cambridge University Press: 26 October 2001
Abstract
Let r1(n) denote the number of representations of the positive integer n as the sum of a square of a positive integer and the square of a positive prime number. We prove an asymptotic evaluation for [sum ]n[les ]xr1(n)2, as x → ∞, thereby improving upon a O-result of Rieger [7]. We further prove an asymptotic formula for the number of positive integers n [les ] x with r1(n) [ges ] 1, which answers a question stated at the end of [7]. Our result in particular shows that for almost all integers represented as the sum of a square and a square of a prime, the representation is unique.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 131 , Issue 1 , July 2001 , pp. 1 - 22
- Copyright
- 2001 Cambridge Philosophical Society
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