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Zeta functions are typically analogues or generalizations of the Riemann zeta function. Examples include Dedekind zeta functions of number fields, and zeta functions of varieties over finite fields. They are typically initially defined as formal generating functions, but often admit analytic continuations.
12
votes
Are there refuted analogues of the Riemann hypothesis?
It is some time ago that I read it, so I hope I recall the details correctly but:
in Eisenstein series and the Riemann zeta function (Automorphic Forms, Representation Theory and Arithmetic, Springer …