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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.
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Fractional powers of Dirichlet series?
Let $R$ be the ring of Dirichlet series with integer coefficients. I'd often wondered about whether $R$ was a UFD; this post cleared that up, because it turns out that $R\simeq\mathbb{Z}[[x_1,x_2,\cdo …