Large sieve estimate for multivariate polynomial moduli and applications

Halupczok, Karin; Munsch, Marc

doi:10.1007/s00605-021-01641-6

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Journal Article

Large sieve estimate for multivariate polynomial moduli and applications

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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
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arXiv:2110.13257.pdf
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Citation

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.

Cite as: http://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.