2020/09/12 by Régis de la Bretèche, de la Bretèche, Régis, Daniel Fiorilli +1
Mathematics · #11M26 (secondary) #11N05 (primary) #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11M26 #msc:11N05
paper · pdf · doi:10.48550/arxiv.2009.05760
15 pages
arxiv created 2020/09/12 · arxiv updated 2020/09/15
We establish lower bounds for all weighted even moments of primes up to X in intervals which are in agreement with a conjecture of Montgomery and Soundararajan. Our bounds hold unconditionally for an unbounded set of values of X, and hold for all X under the Riemann Hypothesis. We also deduce new unconditional Ω-results for the classical prime counting function.