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**Abstract:**

Well known theorems originating from the
1920's established that knowing the zero-free region of the Riemann zeta
function is equivalent to having an upper bound for the discrepancy of the
Farey sequence. It follows that the reduced rationals in the unit interval are
as evenly spaced as possible if and only if the Riemann Hypothesis is true. In
a paper published in 1971 Martin Huxley proved an analogous statement about the
zero free region of any Dirichlet L-function. He showed that the problem of
determining the zero free region of such a function is equivalent to that of
determining an upper bound for a weighted discrepancy of a subset of the Farey
fractions. We will explain all of these facts in more detail and then discuss
recent results about properties of special subsets of the Farey fractions.