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Spring 2009 The behaviour in short intervals of exponential sums over sifted integers
H. Maier, A. Sankaranarayanan
Illinois J. Math. 53(1): 111-133 (Spring 2009). DOI: 10.1215/ijm/1264170842

Abstract

We consider the Hardy–Littlewood approach to the Twin prime problem, which uses a certain exponential sum over prime numbers. We propose a conjecture on the behaviour of the exponential sum in short intervals of the argument. We first show that this conjecture implies the Twin prime conjecture. We then prove that an analogous conjecture is true for exponential sums over integers without small prime factors.

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H. Maier. A. Sankaranarayanan. "The behaviour in short intervals of exponential sums over sifted integers." Illinois J. Math. 53 (1) 111 - 133, Spring 2009. https://doi.org/10.1215/ijm/1264170842

Information

Published: Spring 2009
First available in Project Euclid: 22 January 2010

zbMATH: 1279.11101
MathSciNet: MR2584938
Digital Object Identifier: 10.1215/ijm/1264170842

Subjects:
Primary: 11N25 , 11P32 , 11P55

Rights: Copyright © 2009 University of Illinois at Urbana-Champaign

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Vol.53 • No. 1 • Spring 2009
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