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 ≫ p2/5+o(1) that is the value of an incomplete norm form polynomial.

Large sieve estimate for multivariate polynomial moduli and applications

Munsch M.
2022

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 ≫ p2/5+o(1) that is the value of an incomplete norm form polynomial.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/1079499
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