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The Quarterly Journal of Mathematics Advance Access published online on September 18, 2009
The Quarterly Journal of Mathematics, doi:10.1093/qmath/hap029
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© 2009. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

SPARSE VARIANCE FOR PRIMES IN ARITHMETIC PROGRESSION

J. Brüdern

Institut für Algebra und Zahlentheorie, Universität Stuttgart, D-70511 Stuttgart, Germany

T. D. Wooley{dagger}

School of Mathematics, University of Bristol, University Walk, Clifton, Bristol BS8 1TW, UK

{dagger} Corresponding author. E-mail: Trevor.Wooley{at}bristol.ac.uk

Received 4 May 2009; revised 18 August 2009
  Abstract

An analogue of the Montgomery–Hooley asymptotic formula is established for the variance of the number of primes in arithmetic progressions, in which the moduli are restricted to the values of a polynomial.


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