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Murmurations of modular forms in the weight aspect
Published 11 Oct 2023 in math.NT | (2310.07746v1)
Abstract: We prove the existence of "murmurations" in the family of holomorphic modular forms of level $1$ and weight $k\to\infty$, 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.
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