Murmurations of Dirichlet characters : WestminsterResearch

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Title	Murmurations of Dirichlet characters
Type	Journal article
Authors	Oliver, T., Lee, K.-H. and Pozdnyakov, A.
Abstract	We calculate murmuration densities for two families of Dirichlet characters. The first family contains complex Dirichlet characters normalized by their Gauss sums. Integrating the first density over a geometric interval yields a murmuration function compatible with experimental observations. The second family contains real Dirichlet characters weighted by a smooth function with compact support. We show that the second density exhibits a universality property analogous to Zubrilina's density for holomorphic newforms, and it interpolates the phase transition in the the 1-level density for a symplectic family of L-functions.
Article number	rnae277
Journal	International Mathematics Research Notices
Journal citation	2025 (1)
ISSN	1687-0247
	1073-7928
Year	2024
Publisher	Oxford University Press
Accepted author manuscript	File Access Level Open (open metadata and files)
Digital Object Identifier (DOI)	https://doi.org/10.1093/imrn/rnae277
Web address (URL)	https://academic.oup.com/imrn/article-abstract/2025/1/rnae277/7932774?redirectedFrom=fulltext
Published	06 Jan 2025

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