It is well known that Farey fractions are uniformely distributed in the interval [0,1] and certain estimates on their discrepancy are equivalent to Riemann hypothesis. In this paper the authors obtain new estimates for the difference between the mean value of absolutely continuos functions on the first N Farey numbers and the integral of the function. They show how this estimates are closely linked with Riemann hypothesis. The proofs are based on results in functional and harmonic analysis.
On the uniform distribution (mod 1) of the Farey fractions and lP spaces
CODECA', Paolo;PERELLI, Alberto
1988
Abstract
It is well known that Farey fractions are uniformely distributed in the interval [0,1] and certain estimates on their discrepancy are equivalent to Riemann hypothesis. In this paper the authors obtain new estimates for the difference between the mean value of absolutely continuos functions on the first N Farey numbers and the integral of the function. They show how this estimates are closely linked with Riemann hypothesis. The proofs are based on results in functional and harmonic analysis.File in questo prodotto:
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