Squarefree integers in large arithmetic progressions

2016/01/31 by Ramon M. Nunes, Nunes, Ramon M.
Computer Science · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #Limits and Structures in Graph Theory #math.NT #msc:11L05 #msc:11N37

paper · pdf · doi:10.48550/arxiv.1602.00311

21 pages, no figures. Comments are welcome

arxiv created 2016/01/31 · arxiv updated 2016/02/02

Abstract

We show that the exponent of distribution of the sequence of squarefree numbers in arithmetic progressions of prime modulus is ≥ 2/3 + 1/57, improving a result of Prachar from 1958. Our main tool is an upper bound for certain bilinear sums of exponential sums which resemble Kloosterman sums, going beyond what can be obtained by the Polya-Vinogradov completion method.

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