Lithuanian Mathematical Journal

, Volume 59, Issue 1, pp 96–110 | Cite as

On M-functions for the value-distributions of L-functions

  • Masahiro MineEmail author


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.


L-function value-distribution Bohr–Jessen limit theorem M-function 


primary 11M06 secondary 11M41 



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Authors and Affiliations

  1. 1.Department of MathematicsTokyo Institute of TechnologyTokyoJapan

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