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Mori, Y and Takashima, K (2016)

On the distribution of the leading digit of an: a study via 𝜒2 statistics

Period. Math. Hungar. 73(2), 224-239.

ISSN/ISBN: 0031-5303 DOI: 10.1007/s10998-016-0138-z

Abstract: We investigate irrational rotations with isolated large partial quotients from the point of view of the distribution of the leading digit of an. We prove some mathematical formulae explaining the unusual behavior of the 𝜒2 statistic of the leading digits of an, where log10 a has a single isolated large partial quotient in its continued fraction expansion. We also report that hills appear infinitely often in the graphs of 𝜒2statistics and that there are many different types of shapes of hills.

AUTHOR = {Mori, Yoshiyuki and Takashima, Keizo}, TITLE = {On the distribution of the leading digit of {$a^n$}: a study via {$\chi^2$} statistics}, JOURNAL = {Period. Math. Hungar.}, FJOURNAL = {Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society}, VOLUME = {73}, YEAR = {2016}, NUMBER = {2}, PAGES = {224--239}, ISSN = {0031-5303}, MRCLASS = {11K38 (11A55 11K31)}, MRNUMBER = {3564566}, MRREVIEWER = {Vilius Stak\.enas}, DOI = {10.1007/s10998-016-0138-z}, URL = {}, }

Reference Type: Journal Article

Subject Area(s): Analysis, Number Theory, Statistics