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Notes on universality in short intervals and exponential shifts 关于短区间普遍性和指数移动的说明
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-05-09 DOI: 10.1007/s10986-024-09631-5
Johan Andersson, Ramūnas Garunkštis, Roma Kačinskaitė, Keita Nakai, Łukasz Pańkowski, Athanasios Sourmelidis, Rasa Steuding, Jörn Steuding, Saeree Wananiyakul
{"title":"Notes on universality in short intervals and exponential shifts","authors":"Johan Andersson, Ramūnas Garunkštis, Roma Kačinskaitė, Keita Nakai, Łukasz Pańkowski, Athanasios Sourmelidis, Rasa Steuding, Jörn Steuding, Saeree Wananiyakul","doi":"10.1007/s10986-024-09631-5","DOIUrl":"https://doi.org/10.1007/s10986-024-09631-5","url":null,"abstract":"<p>We improve a recent universality theorem for the Riemann zeta-function in short intervals due to Antanas Laurinčikas with respect to the length of these intervals. Moreover, we prove that the shifts can even have exponential growth. This research was initiated by two questions proposed by Laurinčikas in a problem session of a recent workshop on universality.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"67 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925437","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
Entire solutions of a class of binomial differential equations 一类二项式微分方程的全解
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-05-07 DOI: 10.1007/s10986-024-09632-4
Zhuo Wang, Qingcai Zhang
{"title":"Entire solutions of a class of binomial differential equations","authors":"Zhuo Wang, Qingcai Zhang","doi":"10.1007/s10986-024-09632-4","DOIUrl":"https://doi.org/10.1007/s10986-024-09632-4","url":null,"abstract":"<p>In this paper, we answer the questions posed by Gundersen and Yang about the entire solutions of a class of nonlinear homogeneous binomial differential equations and obtain explicit forms of all the entire solutions of this type of differential equations. Moreover, we provide some examples to demonstrate that the equation solutions we obtained are accurate.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"43 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886309","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 first moment of quadratic Dirichlet L-functions at central values 二次迪里夏特 L 函数中心值的第一矩
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-05-02 DOI: 10.1007/s10986-024-09628-0
Tingting Wen
{"title":"The first moment of quadratic Dirichlet L-functions at central values","authors":"Tingting Wen","doi":"10.1007/s10986-024-09628-0","DOIUrl":"https://doi.org/10.1007/s10986-024-09628-0","url":null,"abstract":"<p>We obtain an asymptotic formula for the smoothly weighted first moment of quadratic Dirichlet <i>L</i>-functions at central values, with explicit main terms and an error term that is “square-root” of the main term.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"85 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140830432","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 the exceptional set for Diophantine inequality with unlike powers of primes 论与素数幂不相似的 Diophantine 不等式的例外集
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-03-19 DOI: 10.1007/s10986-024-09624-4
Huafeng Liu, Rui Liu
{"title":"On the exceptional set for Diophantine inequality with unlike powers of primes","authors":"Huafeng Liu, Rui Liu","doi":"10.1007/s10986-024-09624-4","DOIUrl":"https://doi.org/10.1007/s10986-024-09624-4","url":null,"abstract":"<p>Let <i>λ</i><sub>2</sub>, <i>λ</i><sub>3</sub>, <i>λ</i><sub>4</sub>, <i>λ</i><sub>5</sub> be nonzero real numbers, not all negative. Let <span>(mathfrak{V})</span> be a <i>well-spaced</i> sequence. Assume that <i>λ</i><sub>2</sub>/<i>λ</i><sub>3</sub> is irrational and algebraic, and <i>δ &gt;</i> 0. Let <span>(Eleft(mathfrak{V},N,delta right))</span> be the number of <span>(upsilon in mathfrak{V})</span> with <span>(upsilon le N)</span> such that the Diophantine inequality <span>(left|{lambda }_{2}{p}_{2}^{2}+{lambda }_{3}{p}_{3}^{3}+{lambda }_{4}{p}_{4}^{4}+{lambda }_{5}{p}_{5}^{5}-upsilon right|&lt;{upsilon }^{-delta })</span> has no solution in primes <i>p</i><sub>2</sub>, <i>p</i><sub>3</sub>, <i>p</i><sub>4</sub>, <i>p</i><sub>5</sub>. In this paper, we prove that for any <span>(varepsilon &gt;0,Eleft(mathfrak{V},N,delta right)ll {N}^{1-19/378+2delta +varepsilon },)</span> which refines the previous result.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"153 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140170766","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
Nodal solutions for some semipositone problemsvia bifurcation theory 通过分岔理论求解某些半正交问题的节点解
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-03-14 DOI: 10.1007/s10986-024-09625-3
Yali Zhang, Ruyun Ma
{"title":"Nodal solutions for some semipositone problemsvia bifurcation theory","authors":"Yali Zhang, Ruyun Ma","doi":"10.1007/s10986-024-09625-3","DOIUrl":"https://doi.org/10.1007/s10986-024-09625-3","url":null,"abstract":"<p>We show the existence of nodal solutions of the second-order nonlinear boundary value problem </p><span>$$begin{array}{l}-{u}^{^{primeprime} }left(xright)=lambda left(gleft(uleft(xright)right)+pleft(x,uleft(xright),{u}^{mathrm{^{prime}}}left(xright)right)right),xin left(mathrm{0,1}right), uleft(0right)=uleft(1right)=0,end{array} ({text{P}})$$</span><p>where <i>λ &gt;</i> 0 is a parameter, <i>p</i> : [0, 1]×ℝ<sup>2</sup> → ℝ and <i>g</i> : ℝ →ℝ are continuous functions, and <i>g</i>(0) = 0. For a nonnegative integer <i>k</i>, we say that a solution is nodal if it has only simple zeros in (0, 1) and has exactly <i>k</i>-1 such zeros. Under some suitable conditions, we obtain that there exists <i>λ</i><sub>∗</sub> &gt; 0 (or <i>λ</i><sup>∗</sup> &gt; 0) such that for fixed <i>k</i> ∈ {1, 2,…}, problem (P) has at least one nodal solution for <i>λ</i> ∈ (<i>k</i><sup>2</sup><i>π</i><sup>2</sup>/<i>g</i><sub>∞</sub>, <i>λ</i><sup>∗</sup>) (or <i>λ</i> ∈ (<i>λ</i><sup>∗</sup>,<i> k</i><sup>2</sup><i>π</i><sup>2</sup>/<i>g</i><sub>∞</sub>)), where <i>g</i><sub>∞</sub> = lim<sub>|<i>s</i>|→∞</sub> <i>g</i>(<i>s</i>)/<i>s</i>. The proof of our main results relies on the bifurcation technique.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"15 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140150976","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
Closure under infinitely divisible distribution roots and the Embrechts–Goldie conjecture 无限可分分布根下的闭合与恩布里奇-戈尔迪猜想
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-02-17 DOI: 10.1007/s10986-024-09620-8
Hui Xu, Changjun Yu, Yuebao Wang, Dongya Cheng
{"title":"Closure under infinitely divisible distribution roots and the Embrechts–Goldie conjecture","authors":"Hui Xu, Changjun Yu, Yuebao Wang, Dongya Cheng","doi":"10.1007/s10986-024-09620-8","DOIUrl":"https://doi.org/10.1007/s10986-024-09620-8","url":null,"abstract":"<p>We show that the distribution class ℒ(γ) 𝒪𝒮 is not closed under infinitely divisible distribution roots for γ &gt; 0, that is, we provide some infinitely divisible distributions belonging to the class, whereas the corresponding Lévy distributions do not. In fact, one part of these Lévy distributions belonging to the class 𝒪ℒℒ(γ) have different properties, and the other parts even do not belong to the class 𝒪ℒ. Therefore, combining with the existing related results, we give a completely negative conclusion for the subject and Embrechts–Goldie conjecture. Then we discuss some interesting issues related to the results of this paper.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"102 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758528","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 existence of solutions to higher-order differential equations with nonhomogeneous conditions 非均质条件下高阶微分方程解的存在性
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-02-16 DOI: 10.1007/s10986-024-09622-6
Boddeti Madhubabu, Namburi Sreedhar, Kapula Rajendra Prasad
{"title":"The existence of solutions to higher-order differential equations with nonhomogeneous conditions","authors":"Boddeti Madhubabu, Namburi Sreedhar, Kapula Rajendra Prasad","doi":"10.1007/s10986-024-09622-6","DOIUrl":"https://doi.org/10.1007/s10986-024-09622-6","url":null,"abstract":"<p>We prove the existence and uniqueness of solutions to the differential equations of higher order <span>({x}^{left(lright)}left(sright)+gleft(s,xleft(sright)right)=0,sin left[c,dright],)</span> satisfying three-point boundary conditions that contain a nonhomogeneous term <span>(xleft(cright)=0,{x}{prime}left(cright)=0,{x}^{^{primeprime} }left(cright)=0,dots {x}^{left(l-2right)}left(cright)=0,{x}^{left(l-2right)}left(dright)-{beta x}^{left(l-2right)}left(eta right)=upgamma ,)</span> where <span>(lge mathrm{3,0}le c&lt;eta &lt;d,)</span> the constants <span>(beta ,upgamma )</span> are real numbers, and <span>(g:left[c,dright]times {mathbb{R}}to {mathbb{R}})</span> is a continuous function. By using finer bounds on the integral of kernel, the Banach and Rus fixed point theorems on metric spaces are utilized to prove the existence and uniqueness of a solution to the problem.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"115 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758707","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 theorems for linear processes with tapered innovations and filters 具有锥形创新和滤波器的线性过程的极限定理
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-02-16 DOI: 10.1007/s10986-024-09619-1
{"title":"Limit theorems for linear processes with tapered innovations and filters","authors":"","doi":"10.1007/s10986-024-09619-1","DOIUrl":"https://doi.org/10.1007/s10986-024-09619-1","url":null,"abstract":"<h3>Abstract</h3> <p>We consider the partial-sum process <span> <span>({sum }_{k=1}^{left[ntright]}{X}_{k}^{left(nright)},)</span> </span> where <span> <span>(left{{X}_{k}^{left(nright)}={sum }_{j=0}^{infty }{alpha }_{j}^{left(nright)}{xi }_{k-j}left(bleft(nright)right), kin {mathbb{Z}}right},)</span> </span> <em>n</em> ≥ 1, is a series of linear processes with tapered filter <span> <span>({alpha }_{j}^{left(nright)}={alpha }_{j} {1}_{left{0le jlelambdaleft(nright)right}})</span> </span> and heavy-tailed tapered innovations <em>ξ</em><sub><em>j</em></sub>(<em>b</em>(<em>n</em>)), <em>j ∈</em> Z. Both tapering parameters <em>b</em>(<em>n</em>) and <em>⋋</em> (<em>n</em>) grow to <em>∞</em> as <em>n→∞</em>. The limit behavior of the partial-sum process (in the sense of convergence of finite-dimensional distributions) depends on the growth of these two tapering parameters and dependence properties of a linear process with nontapered filter <em>a</em><sub><em>i</em></sub>, <em>i</em> ≥ 0, and nontapered innovations. We consider the cases where <em>b</em>(<em>n</em>) grows relatively slowly (soft tapering) and rapidly (hard tapering) and all three cases of growth of <em>⋋</em>(<em>n</em>) (strong, weak, and moderate tapering).</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"92 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139772911","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
Rates of convergence in the strong law of large numbers for weighted averages of nonidentically distributed random variables 非同分布随机变量加权平均数的强大数定律收敛速率
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-02-16 DOI: 10.1007/s10986-024-09621-7
{"title":"Rates of convergence in the strong law of large numbers for weighted averages of nonidentically distributed random variables","authors":"","doi":"10.1007/s10986-024-09621-7","DOIUrl":"https://doi.org/10.1007/s10986-024-09621-7","url":null,"abstract":"<h3>Abstract</h3> <p>Integral tests are found for the convergence of two Spitzer-type series associated with a class of weighted averages introduced by Jajte [On the strong law of large numbers, <em>Ann. Probab.</em>, 31(1):409–412, 2003]. Our main theorems are valid for a large family of dependent random variables that are not necessarily identically distributed. As a byproduct, we improve the Marcinkiewicz–Zygmund strong law of large numbers for asymptotically almost negatively associated sequences due to Chandra and Ghosal [Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables <em>Acta Math. Hung.</em>, 71(4):327–336, 1996]. We also complement two limit theorems recently derived by Anh et al. [TheMarcinkiewicz–Zygmund-type strong law of large numbers with general normalizing sequences, <em>J. Theor. Probab.</em>, 34(1):331–348, 2021] and Thành [On a new concept of stochastic domination and the laws of large numbers, <em>Test</em>, 32(1):74–106, 2023]. The obtained results are new even when the summands are independent.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"3 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758574","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
Complete convergence for weighted sums of random variables satisfying generalized Rosenthal-type inequalities* 满足广义罗森塔尔型不等式的随机变量加权和的完全收敛性*
IF 0.4 4区 数学
Lithuanian Mathematical Journal Pub Date : 2024-02-16 DOI: 10.1007/s10986-024-09618-2
Chang Liu, Yu Miao
{"title":"Complete convergence for weighted sums of random variables satisfying generalized Rosenthal-type inequalities*","authors":"Chang Liu, Yu Miao","doi":"10.1007/s10986-024-09618-2","DOIUrl":"https://doi.org/10.1007/s10986-024-09618-2","url":null,"abstract":"<p>In the paper, we establish the complete convergence for weighted sums of random variables satisfying generalized Rosenthal-type inequalities. Our results partially extend some known results and weaken their conditions. As statistical applications, we study the nonparametric regression model and obtain the complete consistency of the weighted regression estimator for the unknown regression functions.</p>","PeriodicalId":51108,"journal":{"name":"Lithuanian Mathematical Journal","volume":"30 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139758706","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
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