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• W2893630296 abstract "A classical problem in number theory is showing that the mean value of an arithmetic function is asymptotic to the mean value over a short interval or over an arithmetic progression, with intervals as short as possible or modulus as large as possible. We study this problem in the function field setting, and prove, for a wide class of arithmetic functions (namely factorization functions), that such an asymptotic result holds, allowing the size of the short interval to be as small as a square-root of the size of the full interval, and similarly for arithmetic progressions. For instance, our results apply for the indicator function of polynomials with a divisor of given degree, and are much stronger than those known for the analogous function over the integers. Results on the variance of the mean values, which give `almost-everywhere' results for much shorter intervals and arithmetic progressions, are also proved." @default.
• W2893630296 created "2018-10-05" @default.
• W2893630296 creator A5056542452 @default.
• W2893630296 date "2018-09-30" @default.
• W2893630296 modified "2023-09-27" @default.
• W2893630296 title "Mean Values of Arithmetic Functions of Polynomials in Short Intervals and in Arithmetic Progressions" @default.
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• W2893630296 hasPublicationYear "2018" @default.
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