## Limit theorems for the Matsumoto zeta-function.(English)Zbl 0859.11053

K. Matsumoto [Lect. Notes Math. 1434, 178-187 (1990; Zbl 0705.11050)] introduced a general zeta-function $$\phi(s)$$, defined by an Euler product, and proved distribution theorems for the frequency with which $$\log\phi (\sigma_0+it)$$ lies in a given set. The present paper generalizes these results by using weighted frequencies.

### MSC:

 11M41 Other Dirichlet series and zeta functions 11K65 Arithmetic functions in probabilistic number theory

Zbl 0705.11050
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### References:

 [1] Bagchi, B., The statistical behaviour and universality properties of the Riemann zeta-function and other allied Dirichlet series, Ph. D. Thesis, Indian Statist. Inst., Calcutta, 1982. [2] Billingsley, P., Convergence of Probability Measures, John Wiley, 1968. · Zbl 0172.21201 [3] Heyer, H., Probability measures on locally compact groups, Springer-Verlag, Berlin-Heidelberg- New York, 1977. · Zbl 0376.60002 [4] Laurinčikas, A., A weighted limit theorem for the Riemann zeta-function, Liet. matem. rink.32(3) (1992), 369-376. (Russian) · Zbl 0805.11061 [5] Matsumoto, K., Value-distribution of zeta-functions, 1434 (1990),178-187. · Zbl 0705.11050 [6] Shabat, B.V., Introduction to complex analysis, Moscow, 1969. (Russian) · Zbl 0422.30001
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