Identities involving Farey fractions |
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Authors: | M N Huxley |
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Institution: | 1.School of Mathematics,University of Cardiff,Cardiff,Wales, UK |
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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. |
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