On sums of fractional parts \(\{na+y\}\)

DOI10.1006/jnth.1997.2080zbMath0886.11045OpenAlexW1967818498MaRDI QIDQ1360709

Christopher G. Pinner

Publication date: 24 July 1997

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1997.2080

zbMATH Keywords

discrepancycontinued fraction expansiongeneralized Zechendorf-expansionOstrowski-expansion

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Irregularities of distribution, discrepancy (11K38) Distribution modulo one (11J71) General theory of distribution modulo (1) (11K06)

Related Items (15)

Local discrepancies in the problem of fractional parts distribution of a linear function ⋮ Geometrization of the Fibonacci numeration system, with applications to number theory ⋮ Embeddings of circular orbits and the distribution of fractional parts ⋮ On the order of magnitude of Sudler products II ⋮ Description and exact maximum and minimum values of the remainder in the problem of the distribution of fractional parts ⋮ On the one-sided boundedness of sums of fractional parts \((\{ n\alpha+ \gamma\}-\frac12)\). ⋮ Nonautonomous bounded remainder sets ⋮ Inverse eigenvalue problems ⋮ Inhomogeneous diophantine approximations and distribution of fractional parts ⋮ Distribution of points of one-dimensional quasilattices with respect to a variable module ⋮ A renormalization approach to irrational rotations ⋮ Local discrepancies in the problem of the distribution of the sequence \(\{k\alpha\}\) ⋮ Тригонометрические суммы над одномерными квазирешетками произвольной коразмерности ⋮ ГЕОМЕТРИЗАЦИЯ ОБОБЩЕННЫХ СИСТЕМ СЧИСЛЕНИЯ ФИБОНАЧЧИ И ЕЕ ПРИЛОЖЕНИЯ К ТЕОРИИ ЧИСЕЛ ⋮ Balance properties of multi-dimensional words

Cites Work

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• The discrepancy of \((n\alpha)_{n\geq 1}\)
• Sums of fractional parts of integer multiples of an irrational
• On the generating function of the integer part: \([n\alpha{}+ \gamma{}\)]
• On the theory of diophantine approximations. I1 (on a problem of A. Ostrowski)
• On the theory of diophantine approximations. II (inhomogeneous problems)
• On the one-sided boundedness of discrepancy function of the sequence {nα}
• Intervalles a restes majorés pour la suite
• Minimum and maximum order of magnitude of the discrepancy of (nα)
• On the discrepancy of (nα)
• On a conjecture of Erdös and Szüsz related to uniform distribution mod 1
• Sur la repartition modulo 1 de la suite nα
• Rational approximations to algebraic numbers

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