Paul P'eringuey

collaborators

4 papers

math.NT2025

Joint distributions of error terms for primes in arithmetic progressions modulo 11

KÃ¼bra Benli, Greg Martin, Paul PÃ©ringuey

We provide a formula for the logarithmic density of the set of positive real numbers on which two prime counting functions $I ¨ (x; q, a)$ and $I ¨ (x; q, b)$ are simultaneously larger tha…

math.NT2025

A note on iterated sumsets races

Paul PÃ©ringuey, Anne de Roton

This short note answers a question raised by Nathanson \cite{Nath25} about "races" between iterated sumsets. We prove that for any integer $n$ , there are finite sets of integers $A…

math.NT2025

Refinements of Artin's primitive root conjecture

A famous conjecture of Artin asserts that any integer $a$ that is neither $- 1$ nor a square should be a primitive root (mod $p$ ) for a positive proportion of primes $p$ . Moreover,…

math.NT2025

Additively stable sets, critical sets for the 3k-4 theorem in $Z$ and $R$

We describe in this paper additively left stable sets, i.e. sets satisfying $((A + A) - in f (A)) \cap [in f (A), sup (A)] = A$ (meaning that $A - in f (A)$ is stable by addition with…

Joint distributions of error terms for primes in arithmetic progressions modulo 11

A note on iterated sumsets races

Refinements of Artin's primitive root conjecture

Additively stable sets, critical sets for the 3k-4 theorem in Z and R

Additively stable sets, critical sets for the 3k-4 theorem in $Z$ and $R$