Article contents
NONNEGATIVE MULTIPLICATIVE FUNCTIONS ON SIFTED SETS, AND THE SQUARE ROOTS OF −1 MODULO SHIFTED PRIMES
Published online by Cambridge University Press: 20 February 2019
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
- Type
- Research Article
- Information
- Copyright
- Copyright © Glasgow Mathematical Journal Trust 2019
References
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20201028144907723-0681:S0017089519000041:S0017089519000041_inline1.gif?pub-status=live)
- 2
- Cited by