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Asymptotic probability measures of Euler products. (English) Zbl 0797.11068

Bombieri, E. (ed.) et al., Proceedings of the Amalfi conference on analytic number theory, held at Maiori, Amalfi, Italy, from 25 to 29 September, 1989. Salerno: Universitá di Salerno, 295-313 (1992).
In a series of papers [Acta Arith. 48, 167-190 (1987; Zbl 0569.10019); Number theory and combinatorics, 1984, 265-278 (1985; Zbl 0608.10040); Acta Arith. 50, 315-337 (1988; Zbl 0657.10042); Nagoya Math. J. 116, 123-138 (1989; Zbl 0694.10038 (675.10017)); Proc. Jap.-Fr. Symp., Tokyo/Jap. 1988, Lecture Notes Math. 1434, 178-187 (1990; Zbl 0705.11050); J. Number Theory 40, 187-210 (1992; Zbl 0746.11051)], the author studied the value distributions of various functions having a Dirichlet series, generalising and extending results by H. Bohr and B. Jessen [Acta Math. 54, 1-35 (1930; JFM 56.0287.01)] on the Riemann zeta function. The present paper is essentially a survey of such results.
For the entire collection see [Zbl 0772.00021].

MSC:

11M41 Other Dirichlet series and zeta functions
11K99 Probabilistic theory: distribution modulo \(1\); metric theory of algorithms
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