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  Large sieve estimate for multivariate polynomial moduli and applications

Halupczok, K., & Munsch, M. (2022). Large sieve estimate for multivariate polynomial moduli and applications. Monatshefte für Mathematik, 197(3), 463-478. doi:10.1007/s00605-021-01641-6.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0009-8F87-E Version Permalink: https://hdl.handle.net/21.11116/0000-000A-3D59-F
Genre: Journal Article

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arXiv:2110.13257.pdf (Preprint), 232KB
 
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 Creators:
Halupczok, Karin, Author
Munsch, Marc1, Author           
Affiliations:
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: 2022
 Publication Status: Issued
 Pages: 16
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 2110.13257
DOI: 10.1007/s00605-021-01641-6
 Degree: -

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Title: Monatshefte für Mathematik
Source Genre: Journal
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Publ. Info: Springer
Pages: - Volume / Issue: 197 (3) Sequence Number: - Start / End Page: 463 - 478 Identifier: -