Large sieve with sparse sets of moduli for \(\mathbb{Z}[i]\)

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 l...

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Bibliographic Details
Published in:arXiv.org 2020-03
Main Authors: Baier, Stephan, Bansal, Arpit
Format: Article
Language:English
Subjects:
Integers
Progressions
Online Access:Get full text
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Summary: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 a recent result by the authors.
ISSN:2331-8422