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NONNEGATIVE MULTIPLICATIVE FUNCTIONS ON SIFTED SETS, AND THE SQUARE ROOTS OF −1 MODULO SHIFTED PRIMES

Part of: Diophantine approximation, transcendental number theory Multiplicative number theory

Published online by Cambridge University Press:  20 February 2019

PAUL POLLACK
PAUL POLLACK*
Affiliation:
Department of Mathematics, University of Georgia, Athens, GA 30602, USA e-mail: pollack@uga.edu
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Abstract

An oft-cited result of Peter Shiu bounds the mean value of a nonnegative multiplicative function over a coprime arithmetic progression. We prove a variant where the arithmetic progression is replaced by a sifted set. As an application, we show that the normalized square roots of −1 (mod m) are equidistributed (mod 1) as m runs through the shifted primes q − 1.

MSC classification

Primary: 11N37: Asymptotic results on arithmetic functions
Secondary: 11N36: Applications of sieve methods 11J71: Distribution modulo one
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Issue 1 , January 2020 , pp. 187 - 199
Copyright
Copyright © Glasgow Mathematical Journal Trust 2019 

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