  The existing periodic orbit theory of spectral correlations for classically
chaotic systems relies on the Riemann-Siegel-like representation of the
spectral determinants which is still largely hypothetical. We suggest a simpler
derivation using analytic continuation of the periodic-orbit expansion of the
pertinent generating function from the convergence border to physically
important real values of its arguments. As examples we consider chaotic systems
without time reversal as well as the Riemann zeta function and Dirichlet
L-functions zeros.
