Computing Extremely Large Values of the Riemann Zeta Function

Abstract

The paper summarizes the computation results pursuing peak values of the Riemann zeta function. The computing method is based on the RS-Peak algorithm by which we are able to solve simultaneous Diophantine approximation problems efficiently. The computation environment was served by the SZTAKI Desktop Grid operated by the Laboratory of Parallel and Distributed Systems at the Hungarian Academy of Sciences and the ATLAS supercomputing cluster of the Eötvös Loránd University, Budapest. We present the largest Riemann zeta value known till the end of 2016.

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Acknowledgments

The authors gratefully acknowledge the constructive comments of Ghaith A. Hiary. We would like to thank the valuable suggestions for the anonymous reviewers. The authors would like to thank the opportunity for accessing to the ATLAS Super Cluster operating at Eötvös Loránd University and for using the capacity of SZTAKI Desktop Grid project operated by the Laboratory of Parallel and Distributed Systems in the Institute for Computer Science and Control of the Hungarian Academy of Sciences.

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Correspondence to Norbert Tihanyi.

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Tihanyi, N., Kovács, A. & Kovács, J. Computing Extremely Large Values of the Riemann Zeta Function. J Grid Computing 15, 527–534 (2017). https://doi.org/10.1007/s10723-017-9416-0

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Keywords

  • Riemann zeta function
  • Distributed computing
  • Large Z(t) values