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Manuscript Title: A program for computing the Riemann Zeta function for complex argument.
Authors: A. Banuelos, R.A. Depine
Program title: RIEMANN ZETA FUNCTION
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.

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

Running time:
Running times < 1s.