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Shintani-Barnes cocycles and values of the zeta functions of algebraic number fields

Leertaste = Abspielen/Pausieren
m = Stumm
f = Vollbild
Pfeil-links = Zurückspulen
Pfeil-rechts = Vorspulen
Hohto Bekki

Shintani-Barnes cocycles and values of the zeta functions of algebraic number fields

The classical Hecke integral formula expresses the zeta function of a number field (of degree g) as an integral of the Eisenstein series over a certain torus of GL(g). In the case where the number field is totally real or totally imaginary, it is known that such an integral formula can be interpreted cohomologically using the Eisenstein cocycles or the Shintani cocycles. In this talk, I would like to discuss the case of general number fields. More precisely, I will explain that by using some ideas and techniques developed in recent works of Vlasenko-Zagier, Charollois-Dasgupta-Greenberg, and Bannai-Hagihara-Yamada-Yamamoto, we can construct a new Eisenstein cocycle which specializes in a uniform way to the values of the zeta functions of general number fields.