Illinois Journal of Mathematics

The behaviour in short intervals of exponential sums over sifted integers

H. Maier and A. Sankaranarayanan

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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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Illinois J. Math., Volume 53, Number 1 (2009), 111-133.

First available in Project Euclid: 22 January 2010

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Zentralblatt MATH identifier

Primary: 11P55: Applications of the Hardy-Littlewood method [See also 11D85] 11P32: Goldbach-type theorems; other additive questions involving primes 11N25: Distribution of integers with specified multiplicative constraints


Maier, H.; Sankaranarayanan, A. The behaviour in short intervals of exponential sums over sifted integers. Illinois J. Math. 53 (2009), no. 1, 111--133. doi:10.1215/ijm/1264170842.

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