An improved result on irregularities in distribution of sequences of integers

John H. Hodges

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1988)

  • Volume: 82, Issue: 1, page 13-16
  • ISSN: 1120-6330

Abstract

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In 1972 the author used a result of K.F. Roth on irregularities in distribution of sequences of real numbers to prove an analogous result related to the distribution of sequences of integers in prescribed residue classes. Here, a 1972 result of W.M. Schmidt, which is an improvement of Roth's result, is used to obtain an improved result for sequences of integers.

How to cite

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Hodges, John H.. "An improved result on irregularities in distribution of sequences of integers." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 82.1 (1988): 13-16. <http://eudml.org/doc/287257>.

@article{Hodges1988,
abstract = {In 1972 the author used a result of K.F. Roth on irregularities in distribution of sequences of real numbers to prove an analogous result related to the distribution of sequences of integers in prescribed residue classes. Here, a 1972 result of W.M. Schmidt, which is an improvement of Roth's result, is used to obtain an improved result for sequences of integers.},
author = {Hodges, John H.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Irregularities; Distribution; Sequences; Integers; irregularities of distribution; sequences of integers},
language = {eng},
month = {3},
number = {1},
pages = {13-16},
publisher = {Accademia Nazionale dei Lincei},
title = {An improved result on irregularities in distribution of sequences of integers},
url = {http://eudml.org/doc/287257},
volume = {82},
year = {1988},
}

TY - JOUR
AU - Hodges, John H.
TI - An improved result on irregularities in distribution of sequences of integers
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1988/3//
PB - Accademia Nazionale dei Lincei
VL - 82
IS - 1
SP - 13
EP - 16
AB - In 1972 the author used a result of K.F. Roth on irregularities in distribution of sequences of real numbers to prove an analogous result related to the distribution of sequences of integers in prescribed residue classes. Here, a 1972 result of W.M. Schmidt, which is an improvement of Roth's result, is used to obtain an improved result for sequences of integers.
LA - eng
KW - Irregularities; Distribution; Sequences; Integers; irregularities of distribution; sequences of integers
UR - http://eudml.org/doc/287257
ER -

References

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  1. HODGES, JOHN H. (1972) - A note on irregularities in distribution of integers, «Portugaliae Mathematica», 31, 171-176. Zbl0242.10017MR311612
  2. NIVEN, IVAN (1961) - Uniform distribution of sequences of integers, «Trans. Amer. Math. Soc.», 98, 52-61. Zbl0096.03102MR120214
  3. ROTH, K.F. (1954) - On irregularities of distribution, «Mathematika», 1, 73-79. Zbl0057.28604MR66435
  4. WOLFGANG, M. (1968) - Irregularities of distribution, «Quart. J. Math., Oxford» (2) 19, 181-191. Zbl0155.37703MR228449
  5. SCHMIDT, WOLFGANG M. (1972) - Irregularities of distribution, VII, «Acta Arithmetica», 21, 45-50. Zbl0244.10035MR319933

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