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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.

MSC:

11N36 Applications of sieve methods
11N05 Distribution of primes
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References:

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