Large sieve estimate for multivariate polynomial moduli and applications

2021/10/25 by Karin Halupczok, Halupczok, Karin, Marc Munsch +1
Mathematics · #11B57 #11L07 #11N32 (Primary) 11C08 #11N36 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2110.13257

openalex publication_date 2021/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 psuch that p-1 has a prime divisor of size ≫ p^2/5+o(1) that is the value of an incomplete norm form polynomial.

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