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Journal Article

Large sieve estimate for multivariate polynomial moduli and applications

MPS-Authors
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Munsch,  Marc
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1007/s00605-021-01641-6
(Publisher version)

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Citation

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.


Cite as: https://hdl.handle.net/21.11116/0000-0009-8F87-E
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.