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.
Official URL: http://www.hindawi.com/jurnals/imrn/volume-2005/S1...
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.
|Subjects:||H - N > Number theory|
|Research Groups:||Number Theory Group|
|Deposited By:||Roger Heath-Brown|
|Deposited On:||15 Jun 2005|
|Last Modified:||20 Jul 2009 14:19|
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