On the theory of M-functions


Salle Kampé de Fériet
Kohji Matsumoto
Nagoya University
Jeudi, 29 Novembre, 2018 - 11:00 - 12:00
M-functions, named by Y. Ihara, are density functions which describe the value-distribution of L-functions. In the case of the Riemann zeta-function, the primitive form of M-functions already appeared in the work of H. Bohr and others in 1930s. In the beginning of the 21st century, Ihara developed a new approach to the theory of M-functions in the case of Dirichlet and Hecke
L-functions, some of which are done jointly with me. In this talk I will survey the results of Bohr, Ihara and others, and l also report some recent developments in the theory of M-functions for other type of zeta and L-functions. In particular I will mention my recent joint researches with Y. Umegaki on the value-distribution of some kind of automorphic L-functions.