Pub Date : 2022-03-01DOI: 10.1007/s10986-022-09560-1
Jonas Kazys Sunklodas
{"title":"On Some Approximations for Sums of Independent Random Variables","authors":"Jonas Kazys Sunklodas","doi":"10.1007/s10986-022-09560-1","DOIUrl":"https://doi.org/10.1007/s10986-022-09560-1","url":null,"abstract":"","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"90 4","pages":"218-238"},"PeriodicalIF":0.4,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138495166","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}
Pub Date : 2022-03-01DOI: 10.1007/s10986-023-09599-8
J. Sunklodas
{"title":"On Some Approximations for Sums of Independent Random Variables","authors":"J. Sunklodas","doi":"10.1007/s10986-023-09599-8","DOIUrl":"https://doi.org/10.1007/s10986-023-09599-8","url":null,"abstract":"","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"62 1","pages":"218 - 238"},"PeriodicalIF":0.4,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45667697","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}
Pub Date : 2022-03-01DOI: 10.1007/s10986-022-09559-8
Muhammad Arif, Mohsan Raza, Inayat Ullah, P. Zaprawa
{"title":"Hankel determinants of order four for a set of functions with bounded turning of order α","authors":"Muhammad Arif, Mohsan Raza, Inayat Ullah, P. Zaprawa","doi":"10.1007/s10986-022-09559-8","DOIUrl":"https://doi.org/10.1007/s10986-022-09559-8","url":null,"abstract":"","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"62 1","pages":"135 - 145"},"PeriodicalIF":0.4,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42565656","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}
Pub Date : 2022-02-16DOI: 10.1007/s10986-022-09574-9
A. Iksanov, A. Marynych, B. Rashytov
{"title":"Stable fluctuations of iterated perturbed random walks in intermediate generations of a general branching process tree*","authors":"A. Iksanov, A. Marynych, B. Rashytov","doi":"10.1007/s10986-022-09574-9","DOIUrl":"https://doi.org/10.1007/s10986-022-09574-9","url":null,"abstract":"","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"62 1","pages":"447 - 466"},"PeriodicalIF":0.4,"publicationDate":"2022-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48047000","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}
Pub Date : 2022-02-03DOI: 10.1007/s10986-022-09553-0
Qing-Long Zhou
For x ∈ [0, 1), let [d1(x), d2(x), . . .] be its Lüroth expansion, and let {pn(x)/qn(x)}n≥1 be the sequence of convergents of x. In this paper, we prove that the Hausdorff dimension of the exceptional set
{"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 ></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":"90 6","pages":""},"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}
Pub Date : 2022-02-02DOI: 10.1007/s10986-022-09554-z
S. Dimitrov
{"title":"The quaternary Piatetski-Shapiro inequality with one prime of the form p = x2 + y2 + 1","authors":"S. Dimitrov","doi":"10.1007/s10986-022-09554-z","DOIUrl":"https://doi.org/10.1007/s10986-022-09554-z","url":null,"abstract":"","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"62 1","pages":"170 - 191"},"PeriodicalIF":0.4,"publicationDate":"2022-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41469885","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}
Pub Date : 2022-02-02DOI: 10.1007/s10986-022-09552-1
Ce Xu, Xixi Zhang, Ying Li
For k ≔ (k1, …, kr) ∈ ℕr and n, m ∈ ℕ, we extend the definition of classical hyperharmonic numbers to define the multiple hyperharmonic numbers ( {zeta}_n^{(m)}(k) ) and the Euler sums of multiple hyperharmonic numbers ζ(m)(q; k)(m + 2 − k1 ≤ q ∈ ℕ). When k = (k) ∈ 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 ( {zeta}_n^{(m)}(k) ) can be expressed in terms combinations of products of polynomial in n of degree at most m − 1 and classical multiple harmonic sums with depth ≤ r, and prove that the Euler sums of multiple hyperharmonic numbers ζ(m) (q; k) can be evaluated by classical multiple zeta values with weight ≤ q + |k| and depth ≤ r + 1.
{"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":"90 8","pages":""},"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}
Pub Date : 2022-02-02DOI: 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":"62 1","pages":"146 - 149"},"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}
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