Murmurations, originally referring to the wave-like patterns in the movement of flocks of starlings, have acquired a new meaning in analytic number theory: a correlation between the Dirichlet coefficients of a family of L-functions and their root numbers. These phenomena were first observed in Elliptic curves by He, Lee, Oliver, and Pozdnyakov in 2022, using machine learning algorithms, and soon in other families of L-functions, including those of Dirichlet characters and automorphic forms, and have been actively studied ever since.

In this talk, I will present joint work with Jonathan Bober, Andrew R. Booker, David Lowry-Duda, Andrei Seymour-Howell, and Nina Zubrilina, demonstrating murmurations in holomorphic modular forms and Maass forms, with a focus on the archimedean aspect.