TY - JOUR

T1 - An amortized-complexity method to compute the Riemann zeta function

AU - Hiary, Ghaith

PY - 2011

Y1 - 2011

N2 - 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 .

AB - 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 .

U2 - http://dx.doi.org/10.1090/S0025-5718-2011-02452-X

DO - http://dx.doi.org/10.1090/S0025-5718-2011-02452-X

M3 - Article (Academic Journal)

SN - 0025-5718

VL - 80

SP - 1785

EP - 1796

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 275

ER -