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.
1988
Codeca', Paolo; Perelli, Alberto
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/522882
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 4
social impact