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dc.contributor.authorBanks, William David, 1964-eng
dc.contributor.authorHeath-Brown, D. R.eng
dc.contributor.authorShparlinski, Igor E.eng
dc.descriptionThis 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.eng
dc.description.abstractWe 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.eng
dc.relation.ispartofMathematics publications (MU)eng
dc.relation.ispartofcommunityUniversity of Missouri-Columbia. College of Arts and Sciences. Department of Mathematicseng
dc.source.urihttp://imrn.oxfordjournals.org/content/2005/1/1.abstract http://www.math.missouri.edu/~bbanks/papers/index.htmleng
dc.subject.lcshNumber theoryeng
dc.subject.lcshExponential sumseng
dc.titleOn the average value of divisor sums in arithmetic progressionseng

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