01-38.pdf (154.36 kB)
The index of Farey sequence
preprint
posted on 2006-01-31, 17:57 authored by R.R. Hall, Peter ShiuWe 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.
History
School
- Science
Department
- Mathematical Sciences
Pages
158066 bytesPublication date
2001Notes
This is a pre-print.Language
- en