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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_0Distribution 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. |

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