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.
2022-01-01
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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