The semiclassical functional equation.
A semiclassical analog of the functional equation for the Riemann zeta function is considered. In the case of the zeta function itself, this equation forms the basis for a finite approximation to the Dirichlet series, known as the approximate functional equation. In the same way, the semiclassical functional equation can be shown to give rise to a finite approximation to the semiclassical representation of the quantum spectral determinant as a sum over classical pseudo-orbits. This finite approximation has been called the Riemann-Siegel look-alike formula. The formal nature of the derivation of this result is discussed and the fact that it appears to imply a remarkable relationship between long and short pseudo-orbits is shown.
Keating
Jonathan
J
Department of Mathematics, The University, Manchester M13 9PL, United Kingdom.