Huxley, Martin Neil 2012. Identities involving Farey fractions. Proceedings of the Steklov Institute of Mathematics 276 (1) , pp. 125-139. 10.1134/S0081543812010105 |
Official URL: http://dx.doi.org/10.1134/S0081543812010105
Abstract
The rational numbers a/q in [0, 1] can be counted by increasing height H(a/q) = max(a, q), or ordered as real numbers. Franel’s identity shows that the Riemann hypothesis is equivalent to a strong bound for a measure of the independence of these two orderings. We give a proof using Dedekind sums that allows weights w(q). Taking w(q) = χ(q) we find an extension to Dirichlet L-functions.
Item Type: | Article |
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Date Type: | Publication |
Status: | Published |
Schools: | Mathematics |
Subjects: | Q Science > QA Mathematics |
Publisher: | Springer |
ISSN: | 0081-5438 |
Last Modified: | 04 Jun 2017 04:01 |
URI: | https://orca.cardiff.ac.uk/id/eprint/30993 |
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