Abstract
We present highlights of computations of the Riemann zeta function around large values and high zeros. The main new ingredient in these computations is an implementation of the second author's fast algorithm for numerically evaluating quadratic exponential sums. In addition, we use a new simple multi-evaluation method to compute the zeta function in a very small range at little more than the cost of evaluation at a single point.
| Original language | English |
|---|---|
| Pages (from-to) | 125-137 |
| Number of pages | 13 |
| Journal | Experimental Mathematics |
| Volume | 27 |
| Issue number | 2 |
| Early online date | 14 Oct 2016 |
| DOIs | |
| Publication status | Published - 3 Apr 2018 |
Keywords
- exponential sums
- large values
- the Riemann zeta function
- the van der Corput iteration
- theta algorithm
Fingerprint
Dive into the research topics of 'New Computations of the Riemann Zeta Function on the Critical Line'. Together they form a unique fingerprint.Equipment
-
HPC (High Performance Computing) and HTC (High Throughput Computing) Facilities
Alam, S. R. (Manager), Williams, D. A. G. (Manager), Eccleston, P. E. (Manager) & Greene, D. (Manager)
Facility/equipment: Facility
Profiles
-
Dr Jonathan W Bober
- School of Mathematics - Heilbronn Senior Research Fellow
- Heilbronn Institute for Mathematical Research
- Pure Mathematics
Person: Academic , Member