Theta and Riemann xi function representations from harmonic oscillator eigensolutions
Mathematical Physics
2009-11-11 v1 math.MP
Abstract
From eigensolutions of the harmonic oscillator or Kepler-Coulomb Hamiltonian we extend the functional equation for the Riemann zeta function and develop integral representations for the Riemann xi function that is the completed classical zeta function. A key result provides a basis for generalizing the important Riemann-Siegel integral formula.
Keywords
Cite
@article{arxiv.math-ph/0612086,
title = {Theta and Riemann xi function representations from harmonic oscillator eigensolutions},
author = {Mark W. Coffey},
journal= {arXiv preprint arXiv:math-ph/0612086},
year = {2009}
}
Comments
15 pages, no figures, appears in Phys. Lett. A