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Consecutive Ratios in Second-Order Linear Recurrence Sequences 二阶线性递归序列中的连续比值
Uniform distribution theory Pub Date : 2022-12-01 DOI: 10.2478/udt-2022-0012
D. Berend, R. Kumar
{"title":"Consecutive Ratios in Second-Order Linear Recurrence Sequences","authors":"D. Berend, R. Kumar","doi":"10.2478/udt-2022-0012","DOIUrl":"https://doi.org/10.2478/udt-2022-0012","url":null,"abstract":"Abstract Let (an)n=0∞ be a second-order linear recurrence sequence with constant coefficient. We study the limit points and asymptotic distribution of the sequence of consecutive ratios an+1/an.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"68 3 1","pages":"51 - 76"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89902560","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
On the Derivative of the Minkowski Question-Mark Function 关于闵可夫斯基问号函数的导数
Uniform distribution theory Pub Date : 2022-12-01 DOI: 10.2478/udt-2022-0014
D. Gayfulin
{"title":"On the Derivative of the Minkowski Question-Mark Function","authors":"D. Gayfulin","doi":"10.2478/udt-2022-0014","DOIUrl":"https://doi.org/10.2478/udt-2022-0014","url":null,"abstract":"Abstract The Minkowski question-mark function ?(x) is a continuous monotonous function defined on [0, 1] interval. It is well known fact that the derivative of this function, if exists, can take only two values: 0 and +∞.It isalso known that the value of the derivative ? (x)atthe point x =[0; a1,a2,...,at,...] is connected with the limit behaviour of the arithmetic mean (a1 +a2 +···+at)/t. Particularly, N. Moshchevitin and A. Dushistova showed that if a1+a2+⋯+at<κ1, {a_1} + {a_2} + cdots + {a_t} < {kappa _1}, where κ1=2log(1+52)/log2=1.3884… {kappa _1} = 2log left( {{{1 + sqrt 5 } over 2}} right)/log 2 = 1.3884 ldots , then ?′(x)=+∞.They also proved that the constant κ1 is non-improvable. We consider a dual problem: how small can be the quantity a1 + a2 + ··· + at − κ1t if we know that ? (x) = 0? We obtain the non-improvable estimates of this quantity.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"126 1","pages":"101 - 126"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88087342","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
AO. Univ. Prof. MAG. Dr. Manfred Kühleitner (1967–2022) An Obituary
Uniform distribution theory Pub Date : 2022-12-01 DOI: 10.2478/udt-2022-0009
N. Brunner, Norbert Kaiblinger, R. Tichy
{"title":"AO. Univ. Prof. MAG. Dr. Manfred Kühleitner (1967–2022) An Obituary","authors":"N. Brunner, Norbert Kaiblinger, R. Tichy","doi":"10.2478/udt-2022-0009","DOIUrl":"https://doi.org/10.2478/udt-2022-0009","url":null,"abstract":"","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"69 1","pages":"195 - 197"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72654855","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
Distribution of Leading Digits of Imaginary Parts of Riemann Zeta Zeros 黎曼ζ零虚部前导数的分布
Uniform distribution theory Pub Date : 2022-12-01 DOI: 10.2478/udt-2022-0016
Y. Ohkubo, O. Strauch
{"title":"Distribution of Leading Digits of Imaginary Parts of Riemann Zeta Zeros","authors":"Y. Ohkubo, O. Strauch","doi":"10.2478/udt-2022-0016","DOIUrl":"https://doi.org/10.2478/udt-2022-0016","url":null,"abstract":"Abstract In this paper we study the distribution of leading digits of imaginary parts of Riemann zeta zeros in the b-adic expansion.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"64 6 1","pages":"161 - 164"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76698402","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
The Seventh International Conference on Uniform Distribution Theory (UDT 2021) 第七届均匀分配理论国际会议(UDT 2021)
Uniform distribution theory Pub Date : 2022-05-31 DOI: 10.2478/udt-2022-0004
Gohar M. M. Kyureghyan, Péter Pál, Nikolay Moshchevitin
{"title":"The Seventh International Conference on Uniform Distribution Theory (UDT 2021)","authors":"Gohar M. M. Kyureghyan, Péter Pál, Nikolay Moshchevitin","doi":"10.2478/udt-2022-0004","DOIUrl":"https://doi.org/10.2478/udt-2022-0004","url":null,"abstract":"The Seventh International Conference on Uniform Distribution Theory was scheduled to take place in Linz, Austria, on July 6–10, 2020. Due to the pandemic situation the conference first had been postponed to February 22–25, 2021, and then even had to be converted into an online conference. Hosting institutions were the Johannes Kepler University (JKU) Linz and the Johann Radon Institute for Computational and Applied Mathematics (RICAM) of the Austrian Academy of Sciences. The homepage of the conference can be found at:","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"160 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86459157","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
Bounds on the size of Progression-Free Sets in ℤ m n n中无进展集大小的界
Uniform distribution theory Pub Date : 2022-05-31 DOI: 10.2478/udt-2022-0005
P. Pach
{"title":"Bounds on the size of Progression-Free Sets in ℤ<i>\u0000 <sub>m</sub>\u0000 <sup>n</sup>\u0000 </i>","authors":"P. Pach","doi":"10.2478/udt-2022-0005","DOIUrl":"https://doi.org/10.2478/udt-2022-0005","url":null,"abstract":"\u0000 In this note we give an overview of the currently known best lower and upper bounds on the size of a subset of ℤ\u0000 n\u0000 m\u0000 avoiding k-term arithmetic progression. We will focus on the case when the length of the forbidden progression is 3. We also formulate some open questions.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78348116","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
Weyl’s Uniform Distribution Under Periodic Perturbation 周期扰动下的Weyl均匀分布
Uniform distribution theory Pub Date : 2022-05-06 DOI: 10.2478/udt-2022-0015
V. Totik
{"title":"Weyl’s Uniform Distribution Under Periodic Perturbation","authors":"V. Totik","doi":"10.2478/udt-2022-0015","DOIUrl":"https://doi.org/10.2478/udt-2022-0015","url":null,"abstract":"Abstract We examine the uniform distribution theory of H. Weyl when there is a periodic perturbation present. As opposed to the classical setting, in this case the conditions for (mod 1) density and (mod 1) uniform distribution turn out to be different.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"1 1","pages":"127 - 160"},"PeriodicalIF":0.0,"publicationDate":"2022-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82041539","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
Linear Complexity of Sequences on Koblitz Curves of Genus 2 2属Koblitz曲线上序列的线性复杂度
Uniform distribution theory Pub Date : 2022-03-25 DOI: 10.48550/arXiv.2203.13523
Vishnupriya Anupindi
{"title":"Linear Complexity of Sequences on Koblitz Curves of Genus 2","authors":"Vishnupriya Anupindi","doi":"10.48550/arXiv.2203.13523","DOIUrl":"https://doi.org/10.48550/arXiv.2203.13523","url":null,"abstract":"Abstract In this paper, we consider the hyperelliptic analogue of the Frobenius endomorphism generator and show that it produces sequences with large linear complexity on the Jacobian of genus 2 curves.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"20 1","pages":"1 - 20"},"PeriodicalIF":0.0,"publicationDate":"2022-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87320812","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
Non-Archimedean Koksma Inequalities, Variation, and Fourier Analysis 非阿基米德Koksma不等式、变异和傅立叶分析
Uniform distribution theory Pub Date : 2022-03-15 DOI: 10.2478/udt-2022-0011
Clayton Petsche, N. Somasunderam
{"title":"Non-Archimedean Koksma Inequalities, Variation, and Fourier Analysis","authors":"Clayton Petsche, N. Somasunderam","doi":"10.2478/udt-2022-0011","DOIUrl":"https://doi.org/10.2478/udt-2022-0011","url":null,"abstract":"Abstract We examine four different notions of variation for real-valued functions defined on the compact ring of integers of a non-Archimedean local field, with an emphasis on regularity properties of functions with finite variation, and on establishing non-Archimedean Koksma inequalities. The first version of variation is due to Taibleson, the second due to Beer, and the remaining two are new. Taibleson variation is the simplest of these, but it is a coarse measure of irregularity and it does not admit a Koksma inequality. Beer variation can be used to prove a Koksma inequality, but it is order-dependent and not translation invariant. We define a new version of variation which may be interpreted as the graph-theoretic variation when a function is naturally extended to a certain subtree of the Berkovich affine line. This variation is order-free and translation invariant, and it admits a Koksma inequality which, for a certain natural family of examples, is always sharper than Beer’s. Finally, we define a Fourier-analytic variation and a corresponding Koksma inequality which is sometimes sharper than the Berkovich-analytic inequality.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"2 1","pages":"21 - 50"},"PeriodicalIF":0.0,"publicationDate":"2022-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90563200","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
Approximation of Discrete Measures by Finite Point Sets 用有限点集逼近离散测度
Uniform distribution theory Pub Date : 2022-02-03 DOI: 10.2478/udt-2023-0003
Christian Weiss
{"title":"Approximation of Discrete Measures by Finite Point Sets","authors":"Christian Weiss","doi":"10.2478/udt-2023-0003","DOIUrl":"https://doi.org/10.2478/udt-2023-0003","url":null,"abstract":"Abstract For a probability measure μ on [0, 1] without discrete component, the best possible order of approximation by a finite point set in terms of the star-discrepancy is &inline as has been proven relatively recently. However, if μ contains a discrete component no non-trivial lower bound holds in general because it is straightforward to construct examples without any approximation error in this case. This might explain, why the approximation of discrete measures on [0, 1] by finite point sets has so far not been completely covered in the existing literature. In this note, we close the gap by giving a complete description for discrete measures. Most importantly, we prove that for any discrete measures (not supported on one point only) the best possible order of approximation is for infinitely many N bounded from below by &inline for some constant 6 ≥ c> 2 which depends on the measure. This implies, that for a finitely supported discrete measure on [0, 1]d the known possible order of approximation &inline is indeed the optimal one.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"33 1","pages":"31 - 38"},"PeriodicalIF":0.0,"publicationDate":"2022-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85554693","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
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