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Manuscript Title: A program for computing the Riemann Zeta function for complex argument.
Authors: A. Banuelos, R.A. Depine
Catalogue identifier: ABVJ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 20(1980)441
Programming language: Fortran.
Computer: IBM 360/50.
Operating system: DOS.
RAM: 25K words
Word size: 32
Keywords: General purpose, Function, Riemann zeta function For complex argument, Fermi-dirac function.
Classification: 4.7.

Nature of problem:
The series expansion that gives a good approach to the Fermi-Dirac function Fsigma(alpha) in the range alpha approximately 0 requires the evaluation of the Zeta function zeta(s) for real argument. However, important mathematical questions concerning with the location of the complex zeros of zeta(s), lead us to construct a program directly applicable to complex values of the argument.

Solution method:
The method of solution is based on the series expansion of Gram and Lindelof, and other known results.

The only restriction arises from the error in the values of the Bernoulli numbers.

Running time:
Running times < 1s.