Mathematica Pannonica
Volume/Issue:
Volume 29_NS3: Issue 2
On Graphical Shapes of χ2 Statistics of Leading Digits of Irrational Rotations
Authors:
Yoshiyuki Mori Department of Applied Mathematics, Okayama University of Science, 1-1 Ridai-cho, Okayama 700-0005, Japan

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and
Keizo Takashima Department of Applied Mathematics, Okayama University of Science, 1-1 Ridai-cho, Okayama 700-0005, Japan

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Pages:
139–148
Online Publication Date:
05 Jun 2023
Publication Date:
07 Dec 2023
Article Category:
Research Article
DOI:
https://doi.org/10.1556/314.2023.00013
Keywords:
Leading digits; large partial quotients; irrational rotations; continued fraction expansion
Open access

We discuss the outline of the shapes of graphs of χ 2 statistics for distributions of leading digits of irrational rotations under some conditions on mth convergent. We give some estimates of important coefficients Lk’s, which determine the graphical shapes of χ2 statistics. This means that the denominator qm of mth convergent and the large partial quotient am+1 determine the outline of shapes of graphs, when we observe values of χ 2 statistics with step qm.

  • [1]

    Mori, Y. and Takashima, K. On the distribution of leading digits of 𝑎𝑛: a study via 𝜒2 statistics. Periodica Math. Hung. 73 (2016), 224–239.

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  • [2]

    Nagayoshi, T. and Takashima, K. On the 𝜒2 statistics of leading digits of irrational rotations with a large first or second partial quotient. Periodica Math. Hung. 80 (2020), 158–171.

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  • [3]

    Nagayoshi, T., Shimaru, N., and Takashima, K. On the 𝜒2 statistics of leading digits of irrational rotations with a large second or third partial quotient. Periodica Math. Hung. 82, to appear.

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  • [4]

    Niederreiter, H. Application of diophantine approximations to numerical integration. In: Diophantine Approximation and Its Applications, C. F. Osgood Ed. Academic Press, New York, 1973, pp. 129–199.

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  • [5]

    Ostrowski, A. Bemerkungen zur Theorie der Diophantischen Approximationen. Abh. Math. Sem. Univ. Hamburg 1 (1922), 77–98.

  • [6]

    Shimaru, N, and Takashima, K. Continued fractions and irrational rotations. Periodica Math. Hung. 76 (2018), 158–171.

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Cover Mathematica Pannonica
Mathematica Pannonica
Print ISSN:
0865-2090
Online ISSN:
2786-0752

Editor in Chief: László TÓTH, University of Pécs, Pécs, Hungary

Honorary Editors in Chief:

  • János PINTZ, HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
  • † Ferenc SCHIPP, Eötvös Loránd University, Budapest, Hungary and University of Pécs, Pécs, Hungary
  • Sándor SZABÓ, University of Pécs, Pécs, Hungary
     

Deputy Editors in Chief:

  • Erhard AICHINGER, JKU Linz, Linz, Austria
  • Ferenc HARTUNG, University of Pannonia, Veszprém, Hungary
  • Ferenc WEISZ, Eötvös Loránd University, Budapest, Hungary

Editorial Board

  • Attila BÉRCZES, University of Debrecen, Debrecen, Hungary
  • István BERKES, Rényi Institute of Mathematics, Budapest, Hungary
  • Károly BEZDEK, University of Calgary, Calgary, Canada
  • György DÓSA, University of Pannonia, Veszprém, Hungary
  • Balázs KIRÁLY – Managing Editor, University of Pécs, Pécs, Hungary
  • Vedran KRCADINAC, University of Zagreb, Zagreb, Croatia 
  • Željka MILIN ŠIPUŠ, University of Zagreb, Zagreb, Croatia
  • Gábor NYUL, University of Debrecen, Debrecen, Hungary
  • Margit PAP, University of Pécs, Pécs, Hungary
  • István PINK, University of Debrecen, Debrecen, Hungary
  • Mihály PITUK, University of Pannonia, Veszprém, Hungary
  • Lukas SPIEGELHOFER, Montanuniversität Leoben, Leoben, Austria
  • Andrea ŠVOB, University of Rijeka, Rijeka, Croatia
  • Csaba SZÁNTÓ, Babeş-Bolyai University, Cluj-Napoca, Romania
  • Jörg THUSWALDNER, Montanuniversität Leoben, Leoben, Austria
  • Zsolt TUZA, University of Pannonia, Veszprém, Hungary

Advisory Board

  • Szilárd RÉVÉSZ – Chair, HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
  • Gabriella BÖHM
  • György GÁT, University of Debrecen, Debrecen, Hungary

University of Pécs,
Faculty of Sciences,
Institute of Mathematics and Informatics
Department of Mathematics
7624 Pécs, Ifjúság útja 6., HUNGARY
(36) 72-503-600 / 4179
ltoth@gamma.ttk.pte.hu

  • Mathematical Reviews
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Mathematica Pannonica
Language English
Size A4
Year of
Foundation		 1990
Volumes
per Year		 1
Issues
per Year		 2
Founder Akadémiai Kiadó
Founder's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)

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