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The Quarterly Journal of Mathematics Advance Access published online on October 30, 2007
The Quarterly Journal of Mathematics, doi:10.1093/qmath/ham044
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© 2007. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

THE AVERAGE VALUE OF DIVISOR SUMS IN ARITHMETIC PROGRESSIONS

V. Blomer{dagger}

Department of Mathematics, University of Toronto, 40 St George Street, Toronto, Ontario, Canada M5S 2E4

{dagger} Corresponding author. E-mail: vblomer{at}math.toronto.edu

Received 9 April 2007; revised 4 June 2007
  Abstract

Let {alpha}(n) denote the Fourier coefficients of cusp forms or the number of divisors of n. Estimates of the type Formula are shown, uniformly in q ≤ X. The methods can be extended to other arithmetic functions, for example, the number of representations of n as a sum of two squares or k-free numbers. As an application, sums of the type {sum}n ≤ X{alpha}(n) {psi}(n) for any q-periodic function {psi} can be estimated non-trivially.


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