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Lithuanian Mathematical Journal最新文献

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On the Distribution of the Digits in Lüroth Expansions 论<s:1>罗斯展开中位数的分布
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2022-02-03 DOI: 10.1007/s10986-022-09553-0
Qing-Long Zhou
{"title":"On the Distribution of the Digits in Lüroth Expansions","authors":"Qing-Long Zhou","doi":"10.1007/s10986-022-09553-0","DOIUrl":"https://doi.org/10.1007/s10986-022-09553-0","url":null,"abstract":"<p>For <i>x ∈</i> [0<i>,</i> 1), let [<i>d</i><sub>1</sub>(<i>x</i>)<i>, d</i><sub>2</sub>(<i>x</i>)<i>, . . .</i>] be its Lüroth expansion, and let {<i>p</i><sub><i>n</i></sub>(<i>x</i>)<i>/qn</i>(<i>x</i>)}<sub><i>n</i>≥1</sub> be the sequence of convergents of <i>x</i>. In this paper, we prove that the Hausdorff dimension of the exceptional set</p><span>$$ {F}_{alpha}^{beta }=left{xin left[left.0,1right)right.:underset{nto infty }{lim}operatorname{inf}frac{log {d}_{n+1}(x)}{-log left|x-frac{p_n(x)}{q_n(x)}right|}=alpha, underset{nto infty }{lim}sup frac{log {d}_{n+1}(x)}{-log left|x-frac{p_n(x)}{q_n(x)}right|}ge beta right} $$</span><p>is (1 <i>− β</i>)<i>/</i>2 or 1 <i>− β</i> according to <i>α &gt;</i> 0 or <i>α</i> = 0. This extends an earlier result of Tan and Zhang.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138495165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The quaternary Piatetski-Shapiro inequality with one prime of the form p = x2 + y2 + 1 一元质数形式为p = x2 + y2 + 1的四元Piatetski-Shapiro不等式
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2022-02-02 DOI: 10.1007/s10986-022-09554-z
S. Dimitrov
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引用次数: 0
Euler sums of multiple hyperharmonic numbers 多个超调和数的欧拉和
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2022-02-02 DOI: 10.1007/s10986-022-09552-1
Ce Xu, Xixi Zhang, Ying Li
{"title":"Euler sums of multiple hyperharmonic numbers","authors":"Ce Xu, Xixi Zhang, Ying Li","doi":"10.1007/s10986-022-09552-1","DOIUrl":"https://doi.org/10.1007/s10986-022-09552-1","url":null,"abstract":"<p>For <i>k</i> ≔ (<i>k</i><sub>1</sub>, …, <i>k</i><sub><i>r</i></sub>) ∈ ℕ<sup><i>r</i></sup> and <i>n</i>, <i>m</i> ∈ ℕ, we extend the definition of classical hyperharmonic numbers to define the multiple hyperharmonic numbers <span>( {zeta}_n^{(m)}(k) )</span> and the Euler sums of multiple hyperharmonic numbers <i>ζ</i><sup>(<i>m</i>)</sup>(<i>q</i>; <i>k</i>)(<i>m</i> + 2 − <i>k</i><sub>1</sub> ≤ <i>q</i> ∈ ℕ). When <b><i>k</i></b> = (<i>k</i>) ∈ ℕ, these sums were first studied by Mezö and Dil around 2010, Dil and Boyadzhiev (2015), and more recently, by Dil, Mezö, and Cenkci, Can, Kargin, Dil, and Soylu, and Li. We show that the multiple hyperharmonic numbers <span>( {zeta}_n^{(m)}(k) )</span> can be expressed in terms combinations of products of polynomial in <i>n</i> of degree at most <i>m −</i> 1 and classical multiple harmonic sums with depth ≤ <i>r</i>, and prove that the Euler sums of multiple hyperharmonic numbers <i>ζ</i><sup>(<i>m</i>)</sup> (<i>q</i>; <b><i>k</i></b>) can be evaluated by classical multiple zeta values with weight ≤ <i>q</i> + <i>|</i><b><i>k</i></b><i>|</i> and depth ≤ <i>r</i> + 1.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138495164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On multiplicative functions that are small on average and zero-free regions for the Riemann zeta function 关于平均较小的乘法函数和黎曼ζ函数的无零区域
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2022-02-02 DOI: 10.1007/s10986-022-09555-y
Marco Aymone
{"title":"On multiplicative functions that are small on average and zero-free regions for the Riemann zeta function","authors":"Marco Aymone","doi":"10.1007/s10986-022-09555-y","DOIUrl":"https://doi.org/10.1007/s10986-022-09555-y","url":null,"abstract":"","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42672449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic behaviors of convolution powers of the Riemann zeta distribution Riemann-zeta分布卷积幂的渐近性态
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2022-01-31 DOI: 10.1007/s10986-023-09585-0
T. Aoyama, Ryuya Namba, Koki Ota
{"title":"Asymptotic behaviors of convolution powers of the Riemann zeta distribution","authors":"T. Aoyama, Ryuya Namba, Koki Ota","doi":"10.1007/s10986-023-09585-0","DOIUrl":"https://doi.org/10.1007/s10986-023-09585-0","url":null,"abstract":"","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47576808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Zero-free regions of the fractional derivatives of the Riemann zeta function 黎曼函数的分数阶导数的无零区域
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2022-01-01 DOI: 10.1007/s10986-022-09551-2
S. Pauli, F. Saidak
{"title":"Zero-free regions of the fractional derivatives of the Riemann zeta function","authors":"S. Pauli, F. Saidak","doi":"10.1007/s10986-022-09551-2","DOIUrl":"https://doi.org/10.1007/s10986-022-09551-2","url":null,"abstract":"","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52932493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Approximation by some subsequences of matrix means 矩阵均值的若干子序列的逼近
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2022-01-01 DOI: 10.1007/s10986-022-09557-w
X. Krasniqi, W. Lenski, B. Szal
{"title":"Approximation by some subsequences of matrix means","authors":"X. Krasniqi, W. Lenski, B. Szal","doi":"10.1007/s10986-022-09557-w","DOIUrl":"https://doi.org/10.1007/s10986-022-09557-w","url":null,"abstract":"","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48105835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Correction to: A Hardy–Ramanujan-type inequality for shifted primes and sifted sets 对移位素数和筛集的Hardy–Ramanujan型不等式的修正
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2021-12-30 DOI: 10.1007/s10986-021-09550-9
Kevin Ford
{"title":"Correction to: A Hardy–Ramanujan-type inequality for shifted primes and sifted sets","authors":"Kevin Ford","doi":"10.1007/s10986-021-09550-9","DOIUrl":"https://doi.org/10.1007/s10986-021-09550-9","url":null,"abstract":"","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49242858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Limit distributions for the maxima of discrete random variables under monotone normalization 单调归一化下离散随机变量最大值的极限分布
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2021-12-03 DOI: 10.1007/s10986-021-09545-6
K. Mitov, S. Nadarajah
{"title":"Limit distributions for the maxima of discrete random variables under monotone normalization","authors":"K. Mitov, S. Nadarajah","doi":"10.1007/s10986-021-09545-6","DOIUrl":"https://doi.org/10.1007/s10986-021-09545-6","url":null,"abstract":"","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47304203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
CQR-based inference for the infinite-variance nearly nonstationary autoregressive models 基于cqr的无限方差近非平稳自回归模型推理
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2021-10-05 DOI: 10.1007/s10986-021-09539-4
Ke-Ang Fu, J.-Y. Ni, Yajuan Dong
{"title":"CQR-based inference for the infinite-variance nearly nonstationary autoregressive models","authors":"Ke-Ang Fu, J.-Y. Ni, Yajuan Dong","doi":"10.1007/s10986-021-09539-4","DOIUrl":"https://doi.org/10.1007/s10986-021-09539-4","url":null,"abstract":"","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45990853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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