On the theory of $M$-functions

par Kohji Matsumoto (Université de Nagoya)

mardi 4 déc. 2018, 10:45 → 11:45 Europe/Paris

Bât. Braconnier, salle 112 (ICJ, Université Lyon 1)

$M$-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.