Abstract
We describe two new algorithms for the efficient and rigorous computation of Dirichlet L-functions and their use to verify the Generalised Riemann Hypothesis for all such L-functions associated with primitive characters of modulus q ≤ 400000. We check, to height, max ({108/q},{A.107/q}+200) with A=7.5 in the case of even characters and A=3.75$ for odd characters. In addition we confirm that no Dirichlet L-function with a modulus q ≤ 2000000 vanishes at its central point.
Original language | English |
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Pages (from-to) | 3009-3027 |
Number of pages | 19 |
Journal | Mathematics of Computation |
Volume | 85 |
Issue number | 302 |
Early online date | 15 Jan 2016 |
DOIs | |
Publication status | Published - Nov 2016 |
Keywords
- Primary 11M26
- Primary 11M06
- Secondary 11P32
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HPC (High Performance Computing) Facility
Susan L Pywell (Manager), Simon A Burbidge (Other), Polly E Eccleston (Other) & Simon H Atack (Other)
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