On Dirchlet's series satisfying Riemann's functional equation.

Marvin I. Knopp

Displaying similar documents to “On Dirchlet's series satisfying Riemann's functional equation.”

Mean values of the Riemann zeta-function and its derivatives.

S.M. Gonek (1984)

Inventiones mathematicae

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On Riemann's Zeta Function.

Daniel Bump, Eugene K.-S. Ng (1986)

Mathematische Zeitschrift

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On Some Relations which are Equivalent to Functional Equations Involving the Riemann Zeta Function.

Fritz Oberhettinger, Kusum L. Soni (1972)

Mathematische Zeitschrift

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A family of deformations of the Riemann xi-function

Masatoshi Suzuki (2013)

Acta Arithmetica

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We introduce a family of deformations of the Riemann xi-function endowed with two continuous parameters. We show that it has rich analytic structure and that its conjectural (mild) zero-free region for some fixed parameter is a sufficient condition for the Riemann hypothesis to hold for the Riemann zeta function.

Note on a paper by H. L. Montgomery (Omega theorems for the Riemann zeta- function).

Ramachandra, K., Sankaranarayanan, A. (1991)

Publications de l'Institut Mathématique. Nouvelle Série

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Horizontal monotonicity of the modulus of the zeta function, L-functions, and related functions

Yu. Matiyasevich, F. Saidak, P. Zvengrowski (2014)

Acta Arithmetica

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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)|...