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Results tagged with l-functions
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user 449628
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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vote
Dirichlet Series that fail to be L-functions
Define the prime zeta function $P(s)$ as
$$
P(s)=\sum_pp^{-s}.
$$
By Möbius inversion, one can verify that (configure $\log$ by specifying $\log\zeta(+\infty)=0$)
$$
P(s)=\sum_{n\ge1}{\mu(n)\over n}\l …
- 1,315