Abstract
Bohr and Jessen proved the existence of a certain limit value regarded as the probability that values of the Riemann zeta function belong to a given region in the complex plane. They also studied the density of the probability, which has been called the M-function since the studies of Ihara and Matsumoto. In this paper, we construct M-functions for the value-distributions of L-functions in a class containing many kinds of zeta and L-functions. Moreover, we improve the estimate on the rate of the convergence of the limit studied by Bohr and Jessen.
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Dedicated to Professors Antanas Laurinčikas and Eugenijus Manstavičius on the occasion of their 70th birthdays
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Mine, M. On M-functions for the value-distributions of L-functions. Lith Math J 59, 96–110 (2019). https://doi.org/10.1007/s10986-019-09425-0
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DOI: https://doi.org/10.1007/s10986-019-09425-0