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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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Shortest/Most elegant proof for $L(1,\chi)\neq 0$
I know it's not an answer to the question, but rather another (probably naive) question suggested by the original question.
It seems to me that proving the prime number theorem for arithmetic progres …