The index of Farey sequence

2006-01-31T17:57:49Z (GMT) by R.R. Hall Peter Shiu
We define an integer valued function of the Farey fractions which we call the index, and we prove two exact formulae involving this. We give asymptotic formulae for the second moment of the index and for the value distribution. Zagier communicated to us a remarkable formula relating the index to Dedekind sums and this yields further asymptotic formulae.