Illinois Journal of Mathematics

The behaviour in short intervals of exponential sums over sifted integers

H. Maier and A. Sankaranarayanan

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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.

Article information

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

Dates
First available in Project Euclid: 22 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1264170842

Digital Object Identifier
doi:10.1215/ijm/1264170842

Mathematical Reviews number (MathSciNet)
MR2584938

Zentralblatt MATH identifier
1279.11101

Subjects
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

Citation

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. https://projecteuclid.org/euclid.ijm/1264170842


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References

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