Moscow Mathematical Journal

Volume 18, Issue 2, April–June 2018 pp. 349–366.

Joint Value Distribution Theorems for the Riemann and Hurwitz Zeta-Functions

Authors: Antanas Laurinčikas (1)
Author institution:(1) Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko str. 24, LT-03225 Vilnius, Lithuania

Summary:

In the paper, a class of functions φ(t) is introduced such that a given pair of analytic functions is approximated simultaneously by shifts ζ(s+iφ(k)), ζ(s+iφ(k), α), k∈ℕ, of the Riemann and Hurwitz zeta-functions with parameter α for which the set {(log p: p is prime), (log(m+α): m∈ℕ₀)} is linearly independent over ℚ. The definition of this class includes an estimate for φ(t) and φ'(t) as well as uniform distribution modulo 1 of the sequence {aφ(k): k∈ℚ}, a≠0.

2010 Math. Subj. Class. Primary: 11M06, 11M35.

Keywords: Hurwitz zeta-function, Riemann zeta-function, uniform distribution modulo 1, universality, weak convergence

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