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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.

1 vote

Nonvanishing of central L-values of quadratic twists?

I suggest you try asking Dipendra Prasad. I have some vague memory that he once told me that (conjecturally) if pi is not self dual then the central value will never vanish.
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