A Bombieri-Vinogradov theorem with products of Gaussian primes as moduli. (English) Zbl 1427.11090

Summary: 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. [R. C. Vaughan, “The Bombieri-Vinogradov theorem”, AIM discussion paper, Preprint] to this setting, we apply the polynomial large sieve inequality that has been proved in [the author, Q. J. Math. 66, No. 2, 529–545 (2015; Zbl 1322.11100)] and which includes recent progress in Vinogradov’s mean value theorem due to S. T. Parsell et al. [Geom. Funct. Anal. 23, No. 6, 1962–2024 (2013; Zbl 1320.11028)]. From the benefit of these improvements, we obtain an extended range for the variables compared to the range obtained from standard arguments only.


11N36 Applications of sieve methods
11N05 Distribution of primes
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