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September 2017 A remark on the conditional estimate for the sum of a prime and a square
Yuta Suzuki
Funct. Approx. Comment. Math. 57(1): 61-76 (September 2017). DOI: 10.7169/facm/1616

Abstract

Hardy and Littlewood conjectured that every sufficiently large integer is either a square or the sum of a prime and a square. Let $E(X)$ be the number of positive integers up to $X\ge4$ for which this property does not hold. We prove \[E(X)\ll X^{1/2}(\log X)^A(\log\log X)^4\] with $A=3/2$ under the Generalized Riemann Hypothesis. This is a small improvement on the previous remarks of Mikawa (1993) and Perelli-Zaccagnini (1995) which claim $A=4,3$ respectively.

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Yuta Suzuki. "A remark on the conditional estimate for the sum of a prime and a square." Funct. Approx. Comment. Math. 57 (1) 61 - 76, September 2017. https://doi.org/10.7169/facm/1616

Information

Published: September 2017
First available in Project Euclid: 28 March 2017

zbMATH: 06864164
MathSciNet: MR3704226
Digital Object Identifier: 10.7169/facm/1616

Subjects:
Primary: 11P32
Secondary: 11P55

Keywords: circle method , Hardy-Littlewood conjecture

Rights: Copyright © 2017 Adam Mickiewicz University

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Vol.57 • No. 1 • September 2017
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