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THE MONTGOMERY–HOOLEY THEOREM IN SHORT INTERVALS

Part of: Multiplicative number theory Additive number theory; partitions

Published online by Cambridge University Press:  02 August 2012

Glyn Harman
Glyn Harman*
Affiliation:
Department of Mathematics, Royal Holloway, University of London, Egham Hill, Egham, Surrey TW20 0EX, U.K. (email: G.Harman@rhul.ac.uk)
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Abstract

In this paper we generalize and extend work by Languasco, Perreli and Zaccagnini on the Montgomery–Hooley theorem in short intervals. We are thus able to obtain asymptotic formulae for the mean-square error in the distribution of general sequences in arithmetic progressions in short intervals. As applications we consider lower and upper bound approximations to the characteristic function of the primes in a short interval and an average over short intervals for the von Mangoldt function.

MSC classification

Secondary: 11N13: Primes in progressions 11N36: Applications of sieve methods 11P55: Applications of the Hardy-Littlewood method
Type
Research Article
Information
Mathematika , Volume 59 , Issue 1 , January 2013 , pp. 129 - 139
Copyright
Copyright © University College London 2012

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