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Questions about generalizations of the Riemann Zeta function of arithmetic interest whose definition relies on meromorphic continuation of special kinds of Dirichlet series, such as Dirichlet L-functions, Artin L-functions, elements of the Selberg class, automorphic L-functions, Shimizu L-functions, p-adic L-functions, etc.

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A question about Kato's explicit reciprocity law

In the paper Iwasawa Theory and F-analytic Lubin-tate $(\phi,\Gamma)$-modules Prop 3.4.2 says that for any $x\in{S}$, there exists (not uniuqely) $f(T)\in{B_{rig,F}^+}$ such that $f(u_n)=\log_{LT}(x …