Fast methods to compute the Riemann zeta function

Details Fast methods to compute the Riemann zeta function Fast methods to compute the Riemann zeta function

2007-11-30

arxiv.org/abs/0711.5005v4

Mathematics

Number Theory

Presentation simplified

Scientific paper

The Riemann zeta function on the critical line can be computed using a straightforward application of the Riemann-Siegel formula, Sch\"onhage's method, or Heath-Brown's method. The complexities of these methods have exponents 1/2, 3/8 (=0.375), and 1/3 respectively. In this paper, three new fast and potentially practical methods to compute zeta are presented. One method is very simple. Its complexity has exponent 2/5. A second method relies on this author's algorithm to compute quadratic exponential sums. Its complexity has exponent 1/3. The third method employs an algorithm, developed in this paper, to compute cubic exponential sums. Its complexity has exponent 4/13 (approximately, 0.307).

Affiliated with

Also associated with

No associations

Rating

Fast methods to compute the Riemann zeta function does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Fast methods to compute the Riemann zeta function, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fast methods to compute the Riemann zeta function will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-703260