An amortized-complexity method to compute the Riemann zeta function

Ghaith Hiary

Research output: Contribution to journalArticle (Academic Journal)

Abstract

A practical method to compute the Riemann zeta function is presented. The method can compute at any points in using an average time of per point. This is the same complexity as the Odlyzko-Schönhage algorithm over that interval. Although the method far from competes with the Odlyzko-Schönhage algorithm over intervals much longer than , it still has the advantages of being elementary, simple to implement, it does not use the fast Fourier transform or require large amounts of storage space, and its error terms are easy to control. The method has been implemented, and results of timing experiments agree with its theoretical amortized complexity of .
Original languageEnglish
Pages (from-to)1785-1796
Number of pages12
JournalMathematics of Computation
Volume80
Issue number275
DOIs
Publication statusPublished - 2011

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