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arXiv · 2110.13257

Large sieve estimate for multivariate polynomial moduli and applications

Karin Halupczok·Marc Munsch
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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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Karin Halupczok, Marc Munsch. 2021-10-25. Large sieve estimate for multivariate polynomial moduli and applications. https://arxiv.org/abs/2110.13257

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