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  Large sieve estimate for multivariate polynomial moduli and applications

Halupczok, K., & Munsch, M. (in press). Large sieve estimate for multivariate polynomial moduli and applications. Monatshefte für Mathematik, Early View Online - Print pending. doi:10.1007/s00605-021-01641-6.

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arXiv:2110.13257.pdf (Preprint), 232KB
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https://doi.org/10.1007/s00605-021-01641-6 (Publisher version)
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 Creators:
Halupczok, Karin, Author
Munsch, Marc1, Author              
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Number Theory
 Abstract: We prove large sieve inequalities with multivariate polynomial moduli and deduce a general Bombieri--Vinogradov type theorem for a class of polynomial moduli having a sufficient number of variables compared to its degree. This sharpens previous results of the first author in two aspects: the range of the moduli as well as the class of polynomials which can be handled. As a consequence, we deduce that there exist infinitely many primes $p$such that $p-1$ has a prime divisor of size $\gg p^{2/5+o(1)}$ that is the value of an incomplete norm form polynomial.

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Language(s): eng - English
 Dates: 2021
 Publication Status: Accepted / In Press
 Pages: -
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 2110.13257
DOI: 10.1007/s00605-021-01641-6
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Title: Monatshefte für Mathematik
Source Genre: Journal
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Publ. Info: Springer
Pages: - Volume / Issue: - Sequence Number: Early View Online - Print pending Start / End Page: - Identifier: -