Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Numerical computations concerning the GRH


Author: David J. Platt
Journal: Math. Comp. 85 (2016), 3009-3027
MSC (2010): Primary 11M26, 11M06; Secondary 11P32
DOI: https://doi.org/10.1090/mcom/3077
Published electronically: January 15, 2016
MathSciNet review: 3522979
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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\leq 400\,000$. We check, to height, $ \textrm {max}\left (\frac {10^8}{q},\frac {A\cdot 10^7}{q}+200\right )$ 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\leq 2\,000\,000$ vanishes at its central point.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 11M26, 11M06, 11P32

Retrieve articles in all journals with MSC (2010): 11M26, 11M06, 11P32


Additional Information

David J. Platt
Affiliation: Heilbronn Institute for Mathematical Research, University of Bristol, University Walk, Bristol, BS8 1TW, United Kingdom
Email: dave.platt@bris.ac.uk

DOI: https://doi.org/10.1090/mcom/3077
Received by editor(s): February 8, 2014
Received by editor(s) in revised form: February 20, 2015, and May 11, 2015
Published electronically: January 15, 2016
Article copyright: © Copyright 2016 American Mathematical Society

American Mathematical Society