2023/10/11 by Bober, Jonathan, Booker, Andrew R., Lee, Min +1 · 4 citations
#11F30 (Primary) #11N64 (Secondary) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2310.07746
We prove the existence of "murmurations" in the family of holomorphic modular forms of level 1 and weight k→∞, that is, correlations between their root numbers and Hecke eigenvalues at primes growing in proportion to the analytic conductor. This is the first demonstration of murmurations in an archimedean family.