The Murmurations

• 成果类型: Article
• 署名作者: Zubrilina, Nina
• 署名单位: Massachusetts Institute of Technology (MIT)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-025-01347-8
• 发表日期: 2025
• 页码: 627-680
• 关键词: FORMS

摘要

We establish the first case of the surprising correlation phenomenon observed in the recent works of He, Lee, Oliver, Pozdnyakov, and Sutherland between Fourier coefficients in families of modular forms and their root numbers. We give a complete description of the resulting correlation functions for holomorphic modular forms of any fixed weight k and examine the asymptotic properties of these functions.