English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Large sieve estimate for multivariate polynomial moduli and applications

MPS-Authors
/persons/resource/persons267694

Munsch,  Marc
Max Planck Institute for Mathematics, Max Planck Society;

External Resource
Fulltext (public)

arXiv:2110.13257.pdf
(Preprint), 232KB

Supplementary Material (public)
There is no public supplementary material available
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: 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.