On the average value of divisor sums in arithmetic progressions

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On the average value of divisor sums in arithmetic progressions

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dc.contributor.author Banks, William David, 1964-
dc.contributor.author Heath-Brown, D. R.
dc.contributor.author Shparlinski, Igor E.
dc.date.accessioned 2011-05-05T22:06:10Z
dc.date.available 2011-05-05T22:06:10Z
dc.date.issued 0000
dc.identifier.uri http://hdl.handle.net/10355/10649
dc.description This is a pre-copy-editing, author-produced PDF of an article accepted for publication in International Mathematics Research Notices. The definitive publisher-authenticated version William D. Banks, Roger Heath-Brown and Igor E. Shparlinski, On the average value of divisor sums in arithmetic progressions, Int Math Res Notices 2005 (1): 1-25, is available online at: http://imrn.oxfordjournals.org/content/2005/1/1.abstract. doi: 10.1155/IMRN.2005.1. © 2005 Hindawi Publishing Corporation. en_US
dc.description.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. en_US
dc.language.iso en_US en_US
dc.relation.ispartof Mathematics publications (MU) en
dc.source.uri http://imrn.oxfordjournals.org/content/2005/1/1.abstract http://www.math.missouri.edu/~bbanks/papers/index.html en_US
dc.subject.lcsh Number theory en_US
dc.subject.lcsh Exponential sums en_US
dc.title On the average value of divisor sums in arithmetic progressions en_US
dc.type Preprint en_US
dc.relation.ispartofcommunity University of Missouri-Columbia. College of Arts and Sciences. Department of Mathematics


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