Uniform distribution theory最新文献_第3页

On a Class of Lacunary Almost Newman Polynomials Modulo P and Density Theorems 一类有缺的几乎纽曼多项式模P和密度定理

Uniform distribution theory Pub Date : 2022-01-10 DOI: 10.2478/udt-2022-0007

D. Dutykh, J. Verger-Gaugry

引用次数: 0

Products of Integers with Few Nonzero Digits 少数非零位数整数的乘积

Uniform distribution theory Pub Date : 2021-12-06 DOI: 10.2478/udt-2022-0006

H. Kaneko, T. Stoll

引用次数: 1

Mahler’s Conjecture on ξ(3/2)nmod 1 马勒猜想ξ(3/2)nmod 1

Uniform distribution theory Pub Date : 2021-12-01 DOI: 10.2478/udt-2021-0007

O. Strauch

引用次数: 2

Divisibility Parameters and the Degree of Kummer Extensions of Number Fields 数域的可分性参数与Kummer扩展的度

Uniform distribution theory Pub Date : 2021-12-01 DOI: 10.2478/udt-2021-0008

Antonella Perucca, Pietro Sgobba, S. Tronto

引用次数: 0

Balance and Pattern Distribution of Sequences Derived from Pseudorandom Subsets of ℤq 伪随机子集衍生序列的平衡与模式分布

Uniform distribution theory Pub Date : 2021-12-01 DOI: 10.2478/udt-2021-0009

Huaning Liu, Arne Winterhof

{"title":"Balance and Pattern Distribution of Sequences Derived from Pseudorandom Subsets of ℤq","authors":"Huaning Liu, Arne Winterhof","doi":"10.2478/udt-2021-0009","DOIUrl":"https://doi.org/10.2478/udt-2021-0009","url":null,"abstract":"Abstract Let q be a positive integer and 𝒮={x0,x1,⋯,xT−1}⊆ℤq={0,1,…,q−1} {scr S} = {{x_0},{x_1}, cdots ,{x_{T - 1}}}subseteq {{rm{mathbb Z}}_q} = {0,1, ldots ,q - 1} with 0≤x0<x1<⋯<xT−1≤q−1. 0 le {x_0} < {x_1} <cdots< {x_{T - 1}} le q - 1. . We derive from S three (finite) sequences: (1) For an integer M ≥ 2let (sn)be the M-ary sequence defined by sn ≡ xn+1 − xn mod M, n =0, 1,...,T − 2. (2) For an integer m ≥ 2let (tn) be the binary sequence defined by sn≡xn+1−xn mod M,n=0,1,⋯,T−2. matrix{{{s_n} equiv {x_{n + 1}} - {x_n},bmod ,M,} & {n = 0,1, cdots ,T - 2.}cr} n =0, 1,...,T − 2. (3) Let (un) be the characteristic sequence of S, tn={1if 1≤xn+1−xn≤m−1,0,otherwise,n=0,1,…,T−2. matrix{{{t_n} = left{{matrix{1 hfill & {{rm{if}},1 le {x_{n + 1}} - {x_n} le m - 1,} hfillcr{0,} hfill & {{rm{otherwise}},} hfillcr}} right.} & {n = 0,1, ldots ,T - 2.}cr} n =0, 1,...,q − 1. We study the balance and pattern distribution of the sequences (sn), (tn)and (un). For sets S with desirable pseudorandom properties, more precisely, sets with low correlation measures, we show the following: (1) The sequence (sn) is (asymptotically) balanced and has uniform pattern distribution if T is of smaller order of magnitude than q. (2) The sequence (tn) is balanced and has uniform pattern distribution if T is approximately un={1if n∈𝒮,0,otherwise,n=0,1,…,q−1. matrix{{{u_n} = left{{matrix{1 hfill & {{rm{if}},n in {scr S},} hfillcr{0,} hfill & {{rm{otherwise}},} hfillcr}} right.} & {n = 0,1, ldots ,q - 1.}cr} . (3) The sequence (un) is balanced and has uniform pattern distribution if T is approximately q2. These results are motivated by earlier results for the sets of quadratic residues and primitive roots modulo a prime. We unify these results and derive many further (asymptotically) balanced sequences with uniform pattern distribution from pseudorandom subsets.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"12 1","pages":"89 - 108"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85046925","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

AO. Univ.-Prof. Dr. Reinhard Winkler (1964–2021) An Obituary AO。Univ.-Prof。莱因哈德·温克勒博士(1964-2021)讣告

Uniform distribution theory Pub Date : 2021-12-01 DOI: 10.2478/udt-2021-0011

M. Goldstern, M. Drmota

引用次数: 0

On Some Properties of Irrational Subspaces 关于无理子空间的一些性质

Uniform distribution theory Pub Date : 2021-07-16 DOI: 10.2478/udt-2022-0002

Vasiliy Neckrasov

引用次数: 1

On the Classification of Solutions of Quantum Functional Equations with Cyclic and Semi-Cyclic Supports 具有循环和半循环支撑的量子泛函方程解的分类

Uniform distribution theory Pub Date : 2021-06-01 DOI: 10.2478/udt-2021-0001

L. Nguyen

引用次数: 0

Uniform Distribution of the Weighted Sum-of-Digits Functions 加权数和函数的均匀分布

Uniform distribution theory Pub Date : 2021-06-01 DOI: 10.2478/udt-2021-0005

Ladislav Misík, S. Porubský, O. Strauch

{"title":"Uniform Distribution of the Weighted Sum-of-Digits Functions","authors":"Ladislav Misík, S. Porubský, O. Strauch","doi":"10.2478/udt-2021-0005","DOIUrl":"https://doi.org/10.2478/udt-2021-0005","url":null,"abstract":"Abstract The higher-dimensional generalization of the weighted q-adic sum-of-digits functions sq,γ(n), n =0, 1, 2,..., covers several important cases of sequences investigated in the theory of uniformly distributed sequences, e.g., d-dimensional van der Corput-Halton or d-dimensional Kronecker sequences. We prove a necessary and sufficient condition for the higher-dimensional weighted q-adic sum-of-digits functions to be uniformly distributed modulo one in terms of a trigonometric product. As applications of our condition we prove some upper estimates of the extreme discrepancies of such sequences, and that the existence of distribution function g(x)= x implies the uniform distribution modulo one of the weighted q-adic sum-of-digits function sq,γ (n), n = 0, 1, 2,... We also prove the uniform distribution modulo one of related sequences h1sq, γ (n)+h2sq,γ (n +1), where h1 and h2 are integers such that h1 + h2 ≠ 0 and that the akin two-dimensional sequence sq,γ (n), sq,γ (n +1) cannot be uniformly distributed modulo one if q ≥ 3. The properties of the two-dimensional sequence sq,γ (n),sq,γ (n +1), n =0, 1, 2,..., will be instrumental in the proofs of the final section, where we show how the growth properties of the sequence of weights influence the distribution of values of the weighted sum-of-digits function which in turn imply a new property of the van der Corput sequence.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"1 1","pages":"93 - 126"},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79639055","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

Insertion in Constructed Normal Numbers 构造正常数的插入

Uniform distribution theory Pub Date : 2021-06-01 DOI: 10.2478/udt-2022-0008

V. Becher

引用次数: 0