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September 2017 A Bombieri--Vinogradov Theorem with products of Gaussian primes as moduli
Karin Halupczok
Funct. Approx. Comment. Math. 57(1): 77-91 (September 2017). DOI: 10.7169/facm/1618

Abstract

We prove a version of the Bombieri--Vinogradov Theorem with certain products of Gaussian primes as moduli, making use of their special form as polynomial expressions in several variables. Adapting Vaughan's proof of the classical Bombieri--Vinogadov Theorem, cp. [10] to this setting, we apply the polynomial large sieve inequality that has been proved in [7] and which includes recent progress in Vinogradov's mean value theorem due to Parsell \emph{et al.} in [9]. From the benefit of these improvements, we obtain an extended range for the variables compared to the range obtained from standard arguments only.

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Karin Halupczok. "A Bombieri--Vinogradov Theorem with products of Gaussian primes as moduli." Funct. Approx. Comment. Math. 57 (1) 77 - 91, September 2017. https://doi.org/10.7169/facm/1618

Information

Published: September 2017
First available in Project Euclid: 28 March 2017

zbMATH: 06864165
MathSciNet: MR3704227
Digital Object Identifier: 10.7169/facm/1618

Subjects:
Primary: 11N36
Secondary: 11N05

Keywords: Bombieri--Vinogradov Theorem , Gaussian primes , polynomial large sieve inequality , polynomial moduli in several variables

Rights: Copyright © 2017 Adam Mickiewicz University

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Vol.57 • No. 1 • September 2017
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