On the average value of divisor sums in arithmetic progressions

On the average value of divisor sums in arithmetic progressions

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 multiplica...

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Veröffentlicht in:International Mathematics Research Notices 2005-01, Vol.2005 (1), p.1-25
Hauptverfasser: Banks, William D., Heath-Brown, Roger, Shparlinski, Igor E.
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container_title International Mathematics Research Notices
container_volume 2005
creator Banks, William D.
Heath-Brown, Roger
Shparlinski, Igor E.
description 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.
doi_str_mv 10.1155/IMRN.2005.1
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source Oxford University Press Journals All Titles (1996-Current); EZB-FREE-00999 freely available EZB journals; Alma/SFX Local Collection
title On the average value of divisor sums in arithmetic progressions
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