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The Thue–Morse continued fractions in characteristic 2 are algebraic 特征2中的Thue–Morse连分式是代数的
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2022-03-04 DOI: 10.4064/aa221212-5-1
Y. Bugeaud, Guo-Niu Han
{"title":"The Thue–Morse continued fractions in characteristic 2 are algebraic","authors":"Y. Bugeaud, Guo-Niu Han","doi":"10.4064/aa221212-5-1","DOIUrl":"https://doi.org/10.4064/aa221212-5-1","url":null,"abstract":"Let $a, b$ be distinct, non-constant polynomials in ${mathbb F}_2 [z]$. Let $xi_{a, b}$ be the power series in ${mathbb F}_2((z^{-1}))$ whose sequence of partial quotients is the Thue-Morse sequence over ${a, b}$. We establish that $xi_{a,b}$ is algebraic of degree $4$.","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45257527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 4
Linear independence criteria for generalized polylogarithms with distinct shifts 具有明显位移的广义多对数的线性独立性准则
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2022-02-28 DOI: 10.4064/aa220307-18-10
Sinnou David, Noriko Hirata-Kohno, M. Kawashima
{"title":"Linear independence criteria for generalized polylogarithms with distinct shifts","authors":"Sinnou David, Noriko Hirata-Kohno, M. Kawashima","doi":"10.4064/aa220307-18-10","DOIUrl":"https://doi.org/10.4064/aa220307-18-10","url":null,"abstract":"For a given rational number x and an integer s ≥ 1 , let us consider a generalized polylogarithmic function, often called the Lerch function, defined by","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45817452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 5
Coprimality of Fourier coefficients of eigenforms 特征形式的傅里叶系数的同质性
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2022-02-08 DOI: 10.4064/aa210817-8-2
Satadal Ganguly, Arvind Kumar, Moni Kumari
{"title":"Coprimality of Fourier coefficients of eigenforms","authors":"Satadal Ganguly, Arvind Kumar, Moni Kumari","doi":"10.4064/aa210817-8-2","DOIUrl":"https://doi.org/10.4064/aa210817-8-2","url":null,"abstract":"1.1. Motivation and the first result. Given two integer-valued sequences a1(n) and a2(n), an interesting question is, how the sequence of the gcd’s (a1(n), a2(n)) behaves; and in particular, how often a1(n) and a2(n) are coprime. For example, if a1(n) = n and a2(n) = φ(n), the Euler’s φ-function, then the density of such integers is zero. This follows from the beautiful result of Erdős [Erd49] given below:","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41794507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A divisor problem for polynomials 多项式的除数问题
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2022-02-04 DOI: 10.4064/aa200528-21-4
Benjamin Klahn
{"title":"A divisor problem for polynomials","authors":"Benjamin Klahn","doi":"10.4064/aa200528-21-4","DOIUrl":"https://doi.org/10.4064/aa200528-21-4","url":null,"abstract":"We characterize all monic polynomials f(x) ∈ Z[x] that have the property that f(p) | f(p), for all sufficiently large primes p ≥ N(f). We also give necessary conditions and a sufficient condition for monic polynomials f(x) ∈ Z[x] to satisfy f(p) | f(p) for all primes p.","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45304365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 a problem of Romanoff type 关于一个Romanoff型问题
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2022-01-30 DOI: 10.4064/aa220207-14-6
Yuchen Ding
{"title":"On a problem of Romanoff type","authors":"Yuchen Ding","doi":"10.4064/aa220207-14-6","DOIUrl":"https://doi.org/10.4064/aa220207-14-6","url":null,"abstract":". Let P and N be the sets of all primes and natural numbers, respectively. In this article, it is proved that there is a positive lower density of the natural numbers which can be represented by the form This solves a problem of Chen and Yang in 2014.","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46470521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A study in quantitative equidistribution on the unit square 单位平方上的定量等分布研究
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2022-01-03 DOI: 10.4064/aa220224-25-7
Max Goering, Christian Weiss
{"title":"A study in quantitative equidistribution on the unit square","authors":"Max Goering, Christian Weiss","doi":"10.4064/aa220224-25-7","DOIUrl":"https://doi.org/10.4064/aa220224-25-7","url":null,"abstract":"The distributional properties of the translation flow on the unit square have been considered in different fields of mathematics, including algebraic geometry and discrepancy theory. One method to quantify equidistribution is to compare the error between the actual time the translation flow spent in specific sets $E subset [0,1]^2$ to the expected time. In this article, we prove that when $E$ is in the algebra generated by convex sets the error is of order at most $log(T)^{1+varepsilon}$ for all but countably many directions. Whenever the direction is badly approximable the bound can be sharpened to $log(T)^{1/2+varepsilon}$. The error estimates we produce are smaller than for general measurable sets as proved by Beck, while our class of examples is larger than in the work of Grepstad-Larcher who obtained the bounded remainder property for their sets. Our proof relies on the duality between local convexity of the boundary and regularity of sections of the flow.","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46709027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Forbidden conductors of $L$-functions and continued fractions of particular form L函数的禁止导体和特殊形式的连分数
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2022-01-01 DOI: 10.4064/aa220721-30-9
J. Kaczorowski, A. Perelli, M. Radziejewski
{"title":"Forbidden conductors of $L$-functions and continued fractions of particular form","authors":"J. Kaczorowski, A. Perelli, M. Radziejewski","doi":"10.4064/aa220721-30-9","DOIUrl":"https://doi.org/10.4064/aa220721-30-9","url":null,"abstract":"","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"78 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70439796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Solvable lattice sums and quadratic Dirichlet $L$-values 可解的格和和二次Dirichlet $L$值
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2022-01-01 DOI: 10.4064/aa201104-31-8
Tao Wei, Xuejun Guo
{"title":"Solvable lattice sums and quadratic Dirichlet $L$-values","authors":"Tao Wei, Xuejun Guo","doi":"10.4064/aa201104-31-8","DOIUrl":"https://doi.org/10.4064/aa201104-31-8","url":null,"abstract":"","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70435147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Finiteness of elasticities of orders in central simple algebras 中心简单代数中阶弹性的有限性
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2022-01-01 DOI: 10.4064/aa211015-14-11
C. Barendrecht
{"title":"Finiteness of elasticities of orders in central simple algebras","authors":"C. Barendrecht","doi":"10.4064/aa211015-14-11","DOIUrl":"https://doi.org/10.4064/aa211015-14-11","url":null,"abstract":"","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70437490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Notes on the module of Euler systems for $p$-adic representations 关于$p$进表示的欧拉系统模块的注释
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2022-01-01 DOI: 10.4064/aa211024-13-6
Ryotaro Sakamoto
{"title":"Notes on the module of Euler systems for $p$-adic representations","authors":"Ryotaro Sakamoto","doi":"10.4064/aa211024-13-6","DOIUrl":"https://doi.org/10.4064/aa211024-13-6","url":null,"abstract":"","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70437769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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