Testing the surrogate zeta-function method

The Zeta Function Method and the Harmonic Oscillator Propagator

We show how the pre-exponential factor of the Feynman propagator for the harmonic oscillator can be computed by the generalized ζ-function method. Besides, we establish a direct equivalence between this method and Schwinger’s propertime method. ⋆ e-mail: [email protected] † e-mail: [email protected] 1 In a recent paper that appeared in this journal [1] the harmonic oscillator propagator was e...

An amortized-complexity method to compute the Riemann zeta function

A practical method to compute the Riemann zeta function is presented. The method can compute ζ(1/2 + it) at any T 1/4 points in [T, T + T 1/4] using an average time of T 1/4+o(1) per point. This is the same complexity as the Odlyzko-Schönhage algorithm over that interval. Although the method far from competes with the Odlyzko-Schönhage algorithm over intervals much longer than T 1/4, it still h...

The Probabilistic Zeta Function

This paper is a summary of results on the PG(s) function, which is the reciprocal of the probabilistic zeta function for finite groups. This function gives the probability that s randomly chosen elements generate a group G, and information about the structure of the group G is embedded in it.

The Fibonacci Zeta Function

We consider the lacunary Dirichlet series obtained by taking the reciprocals of the s-th powers of the Fibonacci numbers. This series admits an analytic continuation to the entire complex plane. Its special values at integral arguments are then studied. If the argument is a negative integer, the value is algebraic. If the argument is a positive even integer, the value is transcendental by Neste...

Mollifying the Riemann Zeta-function