The divisor function in arithmetic progressions modulo prime powers

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Abstract

We study the average value of the divisor function τ(n)for n≤x with n≡a mod q. The divisor function is known to be evenly distributed over arithmetic progressions for all q that are a little smaller than x2/3. We show how to go past this barrier when q=pk for odd primes p and any fixed integer k≥7.

Original languageEnglish
Pages (from-to)898-908
Number of pages11
JournalMathematika
Volume62
Issue number3
DOIs
Publication statusPublished - 2016

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ASJC Scopus subject areas

  • Mathematics(all)

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