Displaying similar documents to “Standard Models of Abstract Intersection Theory for Operators in Hilbert Space”

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

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

Acta Arithmetica

Similarity:

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)|...

A family of deformations of the Riemann xi-function

Masatoshi Suzuki (2013)

Acta Arithmetica

Similarity:

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.