A multimodular algorithm for computing Bernoulli numbers
| dc.creator | Harvey, David | |
| dc.date | 2008-07-08 | |
| dc.date | 2008-10-13 | |
| dc.date.accessioned | 2026-07-07T10:08:58Z | |
| dc.date.available | 2026-07-07T10:08:58Z | |
| dc.description | We describe an algorithm for computing Bernoulli numbers. Using a parallel implementation, we have computed B(k) for k = 10^8, a new record. Our method is to compute B(k) modulo p for many small primes p, and then reconstruct B(k) via the Chinese Remainder Theorem. The asymptotic time complexity is O(k^2 log(k)^(2+epsilon)), matching that of existing algorithms that exploit the relationship between B(k) and the Riemann zeta function. Our implementation is significantly faster than several existing implementations of the zeta-function method. | |
| dc.description | 10 pages, 1 table, requires algorithm2e package; many minor edits, updated timings for correct GMP version, added data for calcbn package | |
| dc.identifier | https://arxiv.org/abs/0807.1347 | |
| dc.identifier | http://arxiv.org/abs/0807.1347 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171183 | |
| dc.subject | Number Theory | |
| dc.subject | 11B68 | |
| dc.title | A multimodular algorithm for computing Bernoulli numbers | |
| dc.type | text |