Acta Mathematica Hungarica
Volume/Issue:
Volume 98: Issue 3
An asymptotic property of gap series. II
Authors:
K. Fukuyama Kobe University Department of Mathematics Rokko, Kobe 657-8501 Japan

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B. Petit Université de Bretagne Occidentale, U.F.R. Sciences et Techniques Département de Mathématiques Brest Cedex 29285 France

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Pages:
245–258
Online Publication Date:
03 Nov 2004
Publication Date:
01 Feb 2002
Article Category:
Research Article
DOI:
https://doi.org/10.1023/a:1022877909906
Keywords:
gap series; law of the iterated logarithm
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Abstract  

An upper bound estimate in the law of the iterated logarithm for Σf(nk ω) where nk+1∫nk≧ 1 + ck-α (α≧0) is investigated. In the case α<1/2, an upper bound had been given by Takahashi [15], and the sharpness of the bound was proved in our previous paper [8]. In this paper it is proved that the upper bound is still valid in case α≧1/2 if some additional condition on {nk} is assumed. As an application, the law of the iterated logarithm is proved when {nk} is the arrangement in increasing order of the set B(τ)={1i1...qτiτ|i1,...,iτ∈N0}, where τ≧ 2, N0=NU{0}, and q1,...,qτ are integers greater than 1 and relatively prime to each others.

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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1950
Volumes
per Year		 3
Issues
per Year		 6
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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