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Numerical Computations Concerning the GRH

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)3009-3027
Number of pages19
JournalMathematics of Computation
Issue number302
Early online date15 Jan 2016
DateAccepted/In press - 11 May 2015
DateE-pub ahead of print - 15 Jan 2016
DatePublished (current) - Nov 2016


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.

    Research areas

  • Primary 11M26, Primary 11M06, Secondary 11P32

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  • Full-text PDF (accepted author manuscript)

    Rights statement: First published in Mathematics of Computation in 2015, published by the American Mathematical Society.

    Accepted author manuscript, 332 KB, PDF document


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