Joint Distribution of primes in multiple short intervals

Speaker: Sun Kai Leung

Date: Tue, Jun 18, 2024

Location: PIMS, University of British Columbia

Conference: Comparative Prime Number Theory

Subject: Mathematics, Number Theory

Class: Scientific

CRG: L-Functions in Analytic Number Theory


Assuming the Riemann hypothesis (RH) and the linear independence conjecture (LI), we show that the weighted count of primes in multiple disjoint short intervals has a multivariate Gaussian logarithmic limiting distribution with weak negative correlation. As a consequence, we derive short-interval counterparts for many important works in the literature of the Shanks–Rényi prime number race, including a sharp phase transition from all races being asymptotically unbiased to the existence of biased races. Our result remains novel, even for primes in a single moving interval, especially under a quantitative formulation of the linear independence conjecture (QLI).

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