Let be the ring of integers in . We may define a homomorphism on the (multiplicative) group of non-zero fractional ideals of as follows. Let be a prime of , let be a uniformizer of and let be the element which is at the place and at all other places. We define:
The Hecke L-series attached to a Grössencharacter of is given by the Euler product over all primes of :
Hecke L-series of this form have an analytic continuation and satisfy a certain functional equation. This fact was first proved by Hecke himself but later was vastly generalized by Tate using Fourier analysis on the ring (what is usually called Tate’s thesis).
|Date of creation||2013-03-22 15:45:19|
|Last modified on||2013-03-22 15:45:19|
|Last modified by||alozano (2414)|