2024/02/01 by Miller, Jeremy, Patzt, Peter, Petersen, Dan +1 · 2 citations
#11R59 #20F36 #55P48 #55U10 #Algebraic Topology (math.AT) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2402.00354
We prove a homological stability theorem for families of discrete groups (e.g. mapping class groups, automorphism groups of free groups, braid groups) with coefficients in a sequence of irreducible algebraic representations of arithmetic groups. The novelty is that the stable range is independent of the choice of representation. Combined with earlier work of Bergström--Diaconu--Petersen--Westerland this proves the Conrey--Farmer--Keating--Rubinstein--Snaith predictions for all moments of the family of quadratic L-functions over function fields, for sufficiently large odd prime powers.