Computing Extremely Large Values of the Riemann Zeta Function
- 57 Downloads
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.
KeywordsRiemann zeta function Distributed computing Large Z(t) values
Unable to display preview. Download preview PDF.
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.
- 5.Gourdon, X.: The 1013-rst zeros of the Riemann Zeta function, and zeros computation at very large height. http://numbers.computation.free.fr/Constants/Miscellaneous/zetazeros1e13-1e24.pdf. Accessed 5 December 2016 (2004)
- 6.Tihanyi, N.: Fast method for locating peak values of the Riemann Zeta function on the critical line. In: Sixteenth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC). IEEE Explorer. https://doi.org/10.1109/SYNASC.2014.20 (2014)
- 7.Odlyzko, A.M.: The 1020-th zero of the riemann zeta function and 175 million of its neighbors. http://www.dtc.umn.edu/∼odlyzko/unpublished/. Accessed 5 December 2016 (1992)
- 8.Bober, J.W., Hiary, G.A.: New computations of the Riemann Zeta function on the critical line. Exp. Math., 27, 1–13 (2016)Google Scholar
- 10.Lenstra, A.K., Lenstra, H. Jr, Lovász, L.: Factoring polynomials with rational coefficients. Math. Ann. 261(4), 515–534 (1982)Google Scholar
- 15.Anderson, D.P.: BOINC: a system for public-resource computing and storage. In: Proceedings of the 5th IEEE/ACM International Workshop on Grid Computing (GRID ’04). IEEE Computer Society, Washington, DC, USAGoogle Scholar
- 16.The SZTAKI desktop grid BOINC project. http://szdg.lpds.sztaki.hu/szdg. Accessed 5 December 2016
- 17.Peak performance of intel CPU’s. http://download.intel.com/support/processors/xeon/sb/xeon_5500.pdf. Accessed 5 December 2016