New Analytical Formulas for the Rank of Farey Fractions and Estimates of the Local Discrepancy

New analytical formulas are derived for the rank and the local discrepancy of Farey fractions. The new rank formula is applicable to all Farey fractions and involves sums of a lower order compared to the searched one. This serves to establish a new unconditional estimate for the local discrepancy of...

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Bibliographic Details
Published in:Mathematics
Main Author: Rogelio Tomás García
Format: Article
Language:English
Published: MDPI AG 2025-01-01
Subjects:
Farey sequence
Riemann Hypothesis
Online Access:https://www.mdpi.com/2227-7390/13/1/140

Internet

https://www.mdpi.com/2227-7390/13/1/140

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