The holomorphic flow of the Riemann zeta function

DOI10.1090/S0025-5718-03-01529-1zbMath1060.37039OpenAlexW2031881374MaRDI QIDQ4452175

A. R. Barnett, Kevin A. Broughan

Publication date: 12 February 2004

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-03-01529-1

zbMATH Keywords

dynamical systemRiemann zeta-functionphase portraitseparatrixplotting techniques

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Special classes of entire functions of one complex variable and growth estimates (30D15) Dynamical aspects of holomorphic foliations and vector fields (37F75) Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory (37-04) Analytic computations (11Y35)

Related Items (3)

Corrigendum to ``The holomorphic flow of the Riemann zeta function ⋮ Linear law for the logarithms of the Riemann periods at simple critical zeta zeros ⋮ Newton flow of the Riemann zeta function: separatrices control the appearance of zeros

Uses Software

• Mathematica
• Matlab

Cites Work

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• Convergence acceleration via combined nonlinear-condensation transformations
• Holomorphic flows on simply connected regions have no limit cycles
• Computational strategies for the Riemann zeta function
• Fast Algorithms for Multiple Evaluations of the Riemann Zeta Function
• On the Zeros of the Riemann Zeta Function in the Critical Strip. IV
• On the Zeros of the Riemann Zeta Function in the Critical Strip
• A new asymptotic representation for ζ(½ + i t ) and quantum spectral determinants

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