发布求助
文献互助 智能选刊 最新文献

Uniform distribution theory最新文献

筛选
英文 中文
Extreme Values of Euler-Kronecker Constants 欧拉-克罗内克常数的极值
Uniform distribution theory Pub Date : 2021-06-01 DOI: 10.2478/udt-2021-0002
Henry H. Kim
{"title":"Extreme Values of Euler-Kronecker Constants","authors":"Henry H. Kim","doi":"10.2478/udt-2021-0002","DOIUrl":"https://doi.org/10.2478/udt-2021-0002","url":null,"abstract":"Abstract In a family of Sn-fields (n ≤ 5), we show that except for a density zero set, the lower and upper bounds of the Euler-Kronecker constants are −(n − 1) log log dK+ O(log log log dK) and loglog dK + O(log log log dK), resp., where dK is the absolute value of the discriminant of a number field K.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"1 1","pages":"41 - 52"},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73449455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The Inequality of Erdős-Turán-Koksma in the Terms of the Functions of the System Γ ℬs Γ系统函数项中Erdős-Turán-Koksma的不等式
Uniform distribution theory Pub Date : 2021-06-01 DOI: 10.2478/udt-2021-0004
Tsvetelina Petrova
{"title":"The Inequality of Erdős-Turán-Koksma in the Terms of the Functions of the System Γ ℬs","authors":"Tsvetelina Petrova","doi":"10.2478/udt-2021-0004","DOIUrl":"https://doi.org/10.2478/udt-2021-0004","url":null,"abstract":"Abstract In the present paper the author uses the function system Γℬsconstructed in Cantor bases to show upper bounds of the extreme and star discrepancy of an arbitrary net in the terms of the trigonometric sum of this net with respect to the functions of this system. The obtained estimations are inequalities of the type of Erdős-Turán-Koksma. These inequalities are very suitable for studying of nets constructed in the same Cantor system.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"1 1","pages":"71 - 92"},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88659781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Density of Oscillating Sequences in the Real Line 实线上振荡序列的密度
Uniform distribution theory Pub Date : 2021-05-19 DOI: 10.2478/udt-2022-0003
Ioannis Tsokanos
{"title":"Density of Oscillating Sequences in the Real Line","authors":"Ioannis Tsokanos","doi":"10.2478/udt-2022-0003","DOIUrl":"https://doi.org/10.2478/udt-2022-0003","url":null,"abstract":"Abstract In this paper we study the density in the real line of oscillating sequences of the form (g(k)⋅F(kα))k∈ℕ, {left( {gleft( k right) cdot Fleft( {kalpha } right)} right)_{k in mathbb{N}}}, where g is a positive increasing function and F a real continuous 1-periodic function. This extends work by Berend, Boshernitzan and Kolesnik [Distribution Modulo 1 of Some Oscillating Sequences I-III] who established differential properties on the function F ensuring that the oscillating sequence is dense modulo 1. More precisely, when F has finitely many roots in [0, 1), we provide necessary and also sufficient conditions for the oscillating sequence under consideration to be dense in ℝ. All the results are stated in terms of the Diophantine properties of α, with the help of the theory of continued fractions.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"86 1","pages":"105 - 130"},"PeriodicalIF":0.0,"publicationDate":"2021-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83219109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 Distribution of αp Modulo One in Quadratic Number Fields 二次数域上αp模1的分布
Uniform distribution theory Pub Date : 2021-04-27 DOI: 10.2478/UDT-2021-0006
S. Baier, D. Mazumder, Marc Technau
{"title":"On the Distribution of αp Modulo One in Quadratic Number Fields","authors":"S. Baier, D. Mazumder, Marc Technau","doi":"10.2478/UDT-2021-0006","DOIUrl":"https://doi.org/10.2478/UDT-2021-0006","url":null,"abstract":"Abstract We investigate the distribution of αp modulo one in quadratic number fields 𝕂 with class number one, where p is restricted to prime elements in the ring of integers of 𝕂. Here we improve the relevant exponent 1/4 obtained by the first- and third-named authors for imaginary quadratic number fields [On the distribution of αp modulo one in imaginary quadratic number fields with class number one, J. Théor. Nombres Bordx. 32 (2020), no. 3, 719–760]) and by the first- and second-named authors for real quadratic number fields [Diophantine approximation with prime restriction in real quadratic number fields, Math. Z. (2021)] to 7/22. This generalizes a result of Harman [Diophantine approximation with Gaussian primes, Q. J. Math. 70 (2019), no. 4, 1505–1519] who obtained the same exponent 7/22 for ℚ (i) by extending his method which gave this exponent for ℚ [On the distribution of αp modulo one. II, Proc. London Math. Soc. 72, (1996), no. 3, 241–260]. Our proof is based on an extension of Harman’s sieve method to arbitrary number fields. Moreover, we need an asymptotic evaluation of certain smooth sums over prime ideals appearing in the above-mentioned work by the first- and second-named authors, for which we use analytic properties of Hecke L-functions with Größencharacters.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"19 1","pages":"1 - 48"},"PeriodicalIF":0.0,"publicationDate":"2021-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78040963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Word Metric, Stationary Measure and Minkowski’s Question Mark Function 词度量、平稳测度与Minkowski问号函数
Uniform distribution theory Pub Date : 2020-12-01 DOI: 10.2478/udt-2020-0009
Uriya Pumerantz
{"title":"Word Metric, Stationary Measure and Minkowski’s Question Mark Function","authors":"Uriya Pumerantz","doi":"10.2478/udt-2020-0009","DOIUrl":"https://doi.org/10.2478/udt-2020-0009","url":null,"abstract":"Abstract Given a countably infinite group G acting on some space X, an increasing family of finite subsets Gn, x∈ X and a function f over X we consider the sums Sn(f, x) = ∑g∈Gnf(gx). The asymptotic behaviour of Sn(f, x) is a delicate problem that was studied under various settings. In the following paper we study this problem when G is a specific lattice in SL (2, ℤ ) acting on the projective line and Gn are chosen using the word metric. The asymptotic distribution is calculated and shown to be tightly connected to Minkowski’s question mark function. We proceed to show that the limit distribution is stationary with respect to a random walk on G defined by a specific measure µ. We further prove a stronger result stating that the asymptotic distribution is the limit point for any probability measure over X pushed forward by the convolution power µ∗n.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"46 1","pages":"23 - 38"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85515896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Extremal Problems for Pairs of Uniformly Distributed Sequences and Integrals with Respect to Copula Measures 关于共轭测度的一致分布序列和积分对的极值问题
Uniform distribution theory Pub Date : 2020-12-01 DOI: 10.2478/udt-2020-0013
F. Durante, J. Fernández-Sánchez, C. Ignazzi, W. Trutschnig
{"title":"On Extremal Problems for Pairs of Uniformly Distributed Sequences and Integrals with Respect to Copula Measures","authors":"F. Durante, J. Fernández-Sánchez, C. Ignazzi, W. Trutschnig","doi":"10.2478/udt-2020-0013","DOIUrl":"https://doi.org/10.2478/udt-2020-0013","url":null,"abstract":"Abstract Motivated by the maximal average distance of uniformly distributed sequences we consider some extremal problems for functionals of type μC↦∫01∫01FdμC, {mu _C} mapsto int_0^1 {{{int_0^1 {Fd} }_mu }_C,} where µC is a copula measure and F is a Riemann integrable function on [0, 1]2 of a specific type. Such problems have been considered in [4] and are of interest in the study of limit points of two uniformly distributed sequences.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"1 1","pages":"99 - 112"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88681691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A curiosity About (−1)[e] +(−1)[2e] + ··· +(−1)[Ne]
Uniform distribution theory Pub Date : 2020-12-01 DOI: 10.2478/udt-2020-0007
F. Amoroso, M. Omarjee
{"title":"A curiosity About (−1)[e] +(−1)[2e] + ··· +(−1)[Ne]","authors":"F. Amoroso, M. Omarjee","doi":"10.2478/udt-2020-0007","DOIUrl":"https://doi.org/10.2478/udt-2020-0007","url":null,"abstract":"Abstract Let α be an irrational real number; the behaviour of the sum SN (α):= (−1)[α] +(−1)[2α] + ··· +(−1)[Nα] depends on the continued fraction expansion of α/2. Since the continued fraction expansion of 2/2 sqrt 2 /2 has bounded partial quotients, SN(2)=O(log(N)) {S_N}left( {sqrt 2 } right) = Oleft( {log left( N right)} right) and this bound is best possible. The partial quotients of the continued fraction expansion of e grow slowly and thus SN(2e)=O(log(N)2log log(N)2) {S_N}left( {2e} right) = Oleft( {{{log {{left( N right)}^2}} over {log ,log {{left( N right)}^2}}}} right) , again best possible. The partial quotients of the continued fraction expansion of e/2 behave similarly as those of e. Surprisingly enough SN(e)=O(log(N)log log(N)) 1188 .","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"70 1","pages":"1 - 8"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83801807","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 Maximum Order Complexity of Thue–Morse and Rudin–Shapiro Sequences along Polynomial Values 沿多项式值的Thue-Morse和Rudin-Shapiro序列的最大阶复杂度
Uniform distribution theory Pub Date : 2020-11-06 DOI: 10.2478/udt-2020-0008
P. Popoli
{"title":"On the Maximum Order Complexity of Thue–Morse and Rudin–Shapiro Sequences along Polynomial Values","authors":"P. Popoli","doi":"10.2478/udt-2020-0008","DOIUrl":"https://doi.org/10.2478/udt-2020-0008","url":null,"abstract":"Abstract Both the Thue–Morse and Rudin–Shapiro sequences are not suitable sequences for cryptography since their expansion complexity is small and their correlation measure of order 2 is large. These facts imply that these sequences are highly predictable despite the fact that they have a large maximum order complexity. Sun and Winterhof (2019) showed that the Thue–Morse sequence along squares keeps a large maximum order complexity. Since, by Christol’s theorem, the expansion complexity of this rarefied sequence is no longer bounded, this provides a potentially better candidate for cryptographic applications. Similar results are known for the Rudin–Shapiro sequence and more general pattern sequences. In this paper we generalize these results to any polynomial subsequence (instead of squares) and thereby answer an open problem of Sun and Winterhof. We conclude this paper by some open problems.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"24 1","pages":"9 - 22"},"PeriodicalIF":0.0,"publicationDate":"2020-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87525798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
A Typical Number is Extremely Non-Normal 一个典型的数字是极不正常的
Uniform distribution theory Pub Date : 2020-06-03 DOI: 10.2478/udt-2022-0001
A. Stylianou
{"title":"A Typical Number is Extremely Non-Normal","authors":"A. Stylianou","doi":"10.2478/udt-2022-0001","DOIUrl":"https://doi.org/10.2478/udt-2022-0001","url":null,"abstract":"Abstract Fix a positive integer N ≥ 2. For a real number x ∈ [0, 1] and a digit i ∈ {0, 1,..., N − 1}, let Πi(x, n) denote the frequency of the digit i among the first nN-adic digits of x. It is well-known that for a typical (in the sense of Baire) x ∈ [0, 1], the sequence of digit frequencies diverges as n →∞. In this paper we show that for any regular linear transformation T there exists a residual set of points x ∈ [0,1] such that the T -averaged version of the sequence (Πi(x, n))n also diverges significantly.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"2 1","pages":"77 - 88"},"PeriodicalIF":0.0,"publicationDate":"2020-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75049864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A Class of Littlewood Polynomials that are Not Lα-Flat 一类非l α-平坦的Littlewood多项式
Uniform distribution theory Pub Date : 2020-06-01 DOI: 10.2478/udt-2020-0003
E. Abdalaoui, M. Nadkarni
{"title":"A Class of Littlewood Polynomials that are Not Lα-Flat","authors":"E. Abdalaoui, M. Nadkarni","doi":"10.2478/udt-2020-0003","DOIUrl":"https://doi.org/10.2478/udt-2020-0003","url":null,"abstract":"Abstract We exhibit a class of Littlewood polynomials that are not Lα-flat for any α ≥ 0. Indeed, it is shown that the sequence of Littlewood polynomials is not Lα-flat, α ≥ 0, when the frequency of −1 is not in the interval ] 14 {1 over 4} , 34 {3 over 4} [ We further obtain a generalization of Jensen-Jensen-Hoholdt’s result by establishing that the sequence of Littlewood polynomials is not Lα-flat for any α> 2 if the frequency of −1 is not 12 {1 over 2} . Finally, we prove that the sequence of palindromic Littlewood polynomials with even degrees are not Lα-flat for any α ≥ 0, and we provide a lemma on the existence of c-flat polynomials.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"90 1","pages":"51 - 74"},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87527117","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信