The Mathematical Institute, University of Oxford, Eprints Archive

On the average value of divisor sums in arithmetic progressions

Heath-Brown, D. R. and Banks, W. D. and Shparlinski, I. E. (2005) On the average value of divisor sums in arithmetic progressions. International Mathematics Research Notices (1). pp. 1-25.

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Official URL: http://www.hindawi.com/jurnals/imrn/volume-2005/S1...

Abstract

We consider very short sums of the divisor function in arithmetic progressions prime to a fixed modulus and show that ``on average'' these sums are close to the expected value. We also give applications of our result to sums of the divisor function twisted with characters (both additive and multiplicative) taken on the values of various functions, such as rational and exponential functions; in particular, we obtain upper bounds for such twisted sums.

Item Type:Article
Subjects:H - N > Number theory
Research Groups:Number Theory Group
ID Code:180
Deposited By:Roger Heath-Brown
Deposited On:15 Jun 2005
Last Modified:20 Jul 2009 14:19

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