Large sieve with sparse sets of moduli for $\mathbb{Z}[i]$
Volume 196 / 2020
Acta Arithmetica 196 (2020), 17-34
MSC: 11L40, 11N35.
DOI: 10.4064/aa190329-10-3
Published online: 9 July 2020
Abstract
We establish a general large sieve inequality with sparse sets $\mathcal {S}$ of moduli in the Gaussian integers which are in a sense well-distributed in arithmetic progressions. This extends earlier work of S. Baier on the large sieve with sparse sets of moduli. We then use this result to obtain large sieve bounds for the cases when $\mathcal {S}$ consists of squares of Gaussian integers and of Gaussian primes. Our bound for the case of square moduli improves our recent result [Int. J. Number Theory 14 (2018)].
