Malliavin-type remainders for Beurling generalized prime number systems

Gregory Debruyne
Ghent University, Belgium
https://cage.ugent.be/~gdbruyne/

Date(s) : 08/06/2021 iCal
11h00 - 12h00

A Beurling generalized prime number system is an unbounded sequence 1 < p₁ ≤ p₂ ≤ …. These form the generalized primes of the system and the generalized integers are formed by taking finite products of the generalized primes (including the empty product 1).

We shall discuss several topics than one may study in this setting, with some special attention to Malliavin-type remainders. Let N denote the (generalized) integer counting function, let a, c > 0 and 0 < ɑ ≤ 1. What information does an estimate N(x) = ax + O(x exp(-c log^ɑ x)) provide on the (generalized) primes and vice-versa?