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A probabilistic study on the value-distribution of Dirichlet series attached to certain cusp forms. (English) Zbl 0675.10017
Bohr-Jessen’s classical theorem on the value-distribution of the Riemann zeta-function is generalized to the case of zeta-functions defined by Hecke operators. Bohr-Jessen’s original argument on the sums of closed convex curves has no power in this case, so the author uses Prokhorov’s result on the tightness of probability measures, which gives a proof applicable to a fairly general class of Euler products.
Reviewer: K.Matsumoto

MSC:
11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
11F11 Holomorphic modular forms of integral weight
11M35 Hurwitz and Lerch zeta functions
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