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Identities involving Farey fractions

Huxley, Martin Neil 2012. Identities involving Farey fractions. Proceedings of the Steklov Institute of Mathematics 276 (1) , pp. 125-139. 10.1134/S0081543812010105

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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
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: http://orca.cf.ac.uk/id/eprint/30993

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