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I would like to know if there is any difference between
(1) an algebraic Hecke character
(2) a Hecke character
(3) a Grössencharakter
All of the above in the setting of ellitpic curves with complex multiplication. Thanks!

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It is not clear what that means "in the setting of elliptic curves with CM". – Marc Palm Jul 3 '13 at 9:47
What I meant to say was that in elliptic curves, we have associated grossencharacters and hecke characters. So the question is: are they different? Or are they just different names for the same thing? – BlackAdder Jul 3 '13 at 9:51
Grossencharacters are "grossen" in that they have infinite order. Sometimes "Hecke characters" only means ones of finite order. From the adelic standpoint, authors are less likely to make a distinction. – kantelope Dec 8 '15 at 22:50
up vote 2 down vote accepted

Grossencharacters and Hecke characters are different names for the same thing.

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