The joint universality and the generalized strong recurrence for Dirichlet L-functions
Takashi Nakamura (2009)
Acta Arithmetica
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Displaying similar documents to “On the structure of the Selberg class, VI: non-linear twists”
The joint universality and the generalized strong recurrence for Dirichlet L-functions
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Yu. Matiyasevich, F. Saidak, P. Zvengrowski (2014)
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As usual, let s = σ + it. For any fixed value of t with |t| ≥ 8 and for σ < 0, we show that |ζ(s)| is strictly decreasing in σ, with the same result also holding for the related functions ξ of Riemann and η of Euler. The following inequality related to the monotonicity of all three functions is proved: ℜ (η'(s)/η(s)) < ℜ (ζ'(s)/ζ(s)) < ℜ (ξ'(s)/ξ(s)). It is also shown that extending the above monotonicity result for |ζ(s)|, |ξ(s)|, or |η(s)|...
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