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Acta Arithmetica最新文献

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Dynamics of $mathscr B$-free systems generated by Behrend sets. I Behrend集生成的$mathscr B$ free系统的动力学。我
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2022-05-17 DOI: 10.4064/aa220525-14-2
S. Kasjan, Mariusz Lema'nczyk, S. Z. Alterman
{"title":"Dynamics of $mathscr B$-free systems generated by Behrend sets. I","authors":"S. Kasjan, Mariusz Lema'nczyk, S. Z. Alterman","doi":"10.4064/aa220525-14-2","DOIUrl":"https://doi.org/10.4064/aa220525-14-2","url":null,"abstract":"We study the complexity of $mathscr{B}$-free subshifts which are proximal and of zero entropy. Such subshifts are generated by Behrend sets. The complexity is shown to achieve any subexponential growth and is estimated for some classical subshifts (prime and semiprime subshifts). We also show that $mathscr{B}$-admissible subshifts are transitive only for coprime sets $mathscr{B}$ which allows one to characterize dynamically the subshifts generated by the Erd\"os sets.","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70439725","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
Correspondance de Langlands locale $p$-adiqueet anneaux de Kisin Langlands本地匹配$P$-Adiqueet Kisin戒指
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2022-04-24 DOI: 10.4064/aa220520-24-4
P. Colmez, Gabriel Dospinescu, Wiesława Nizioł
{"title":"Correspondance de Langlands locale $p$-adique\u0000et anneaux de Kisin","authors":"P. Colmez, Gabriel Dospinescu, Wiesława Nizioł","doi":"10.4064/aa220520-24-4","DOIUrl":"https://doi.org/10.4064/aa220520-24-4","url":null,"abstract":"We use a ${mathcal B}$-adic completion and the $p$-adic local Langlands correspondence for ${mathrm {GL}}_2({mathbf Q}_p )$ to give a construction of Kisin's rings and the attached universal Galois representations (in dimension 2 and for ${mathbf Q}_p$) directly from the classical Langlands correspondence. This gives, in particular, a uniform proof of the geometric Breuil-M'ezard conjecture in the supercuspidal case.","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47956787","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
The Hausdorff and packing measure of some digital expansions 一些数字扩展的豪斯多夫和包装度量
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2022-04-10 DOI: 10.4064/aa220124-25-11
Daniel Ingebretson
{"title":"The Hausdorff and packing measure of some digital expansions","authors":"Daniel Ingebretson","doi":"10.4064/aa220124-25-11","DOIUrl":"https://doi.org/10.4064/aa220124-25-11","url":null,"abstract":"interval centered in C ( n, l ) with U / ∈ φ i ([0 , 1]) for all i ∈ I . We will show that d ( U ) ≥ 2 − s by finite induction on the number of level-one basic intervals that intersect U .","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44837556","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
Solutions of certain meta-Fibonacci recurrences 某些元斐波那契递归式的解
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2022-04-08 DOI: 10.4064/aa220613-19-1
Bartosz Sobolewski, M. Ulas
{"title":"Solutions of certain meta-Fibonacci recurrences","authors":"Bartosz Sobolewski, M. Ulas","doi":"10.4064/aa220613-19-1","DOIUrl":"https://doi.org/10.4064/aa220613-19-1","url":null,"abstract":"In this note we investigate the solutions of certain meta-Fibonacci recurrences of the form $f(n)=f(n-f(n-1))+f(n-2)$ for various sets of initial conditions. In the case when $f(n)=1$ for $nleq 1$, we prove that the resulting integer sequence is closely related to the function counting binary partitions of a certain type.","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41511001","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
Multiplicative complements I 乘法补I
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2022-04-01 DOI: 10.4064/aa220408-3-1
Anett Kocsis, D'avid Matolcsi, Csaba S'andor, Gyorgy THotHos
{"title":"Multiplicative complements I","authors":"Anett Kocsis, D'avid Matolcsi, Csaba S'andor, Gyorgy THotHos","doi":"10.4064/aa220408-3-1","DOIUrl":"https://doi.org/10.4064/aa220408-3-1","url":null,"abstract":"In this paper, we study how dense a multiplicative basis of order $h$ for $mathbb{Z}^+!$ can be, improving on earlier results. Upon introducing the notion of a textit{multiplicative complement}, we present some tight density bounds.","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45620829","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: 1
The distribution of rational points on conics 二次曲线上有理点的分布
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2022-03-25 DOI: 10.4064/aa220325-2-8
D. R. Heath-Brown
{"title":"The distribution of rational points on conics","authors":"D. R. Heath-Brown","doi":"10.4064/aa220325-2-8","DOIUrl":"https://doi.org/10.4064/aa220325-2-8","url":null,"abstract":"We examine the counting function for rational points on conics, and show how the point where the asymptotic behaviour begins depends on the size of the smallest zero.","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43298251","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
Transcendence and continued fraction expansionof values of Hecke–Mahler series Hecke-Mahler级数值的超越与连分式展开性
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2022-03-24 DOI: 10.4064/aa220323-18-1
Y. Bugeaud, M. Laurent
{"title":"Transcendence and continued fraction expansion\u0000of values of Hecke–Mahler series","authors":"Y. Bugeaud, M. Laurent","doi":"10.4064/aa220323-18-1","DOIUrl":"https://doi.org/10.4064/aa220323-18-1","url":null,"abstract":"Let $theta$ and $rho$ be real numbers with $0 le theta, rho<1$ and $theta$ irrational. We show that the Hecke-Mahler series $$ F_{theta, rho} (z_1, z_2) = sum_{k_1 ge 1} , sum_{k_2 = 1}^{lfloor k_1 theta + rho rfloor} , z_1^{k_1} z_2^{k_2}, $$ where $lfloor cdot rfloor$ denotes the integer part function, takes transcendental values at any algebraic point $(beta, alpha)$ with $0<|beta|, |beta alpha^theta |<1$. This extends earlier results of Mahler (1929) and Loxton and van der Poorten (1977), who settled the case $rho=0$. Furthermore, for positive integers $b$ and $a$, with $b ge 2$ and $a$ congruent to $1$ modulo $b-1$, we give the continued fraction expansion of the number $$ {(b-1)^2over b} F_{theta, rho} left({1over b}, {1over a}right)+{lfloor theta+rhorfloor(b-1)over b^2a}, $$ from which we derive a formula giving the irrationality exponent of $F_{theta, rho} (1/b, 1/a)$.","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42385359","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
Hyperbolicity of the moduli of certain Fano threefolds 某些Fano三重模的双曲性
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2022-03-21 DOI: 10.4064/aa220322-22-9
Philipp Licht
{"title":"Hyperbolicity of the moduli of certain Fano threefolds","authors":"Philipp Licht","doi":"10.4064/aa220322-22-9","DOIUrl":"https://doi.org/10.4064/aa220322-22-9","url":null,"abstract":"We prove the Shafarevich conjecture for Fano threefolds of Picard rank 1, index 1 and degree 4.","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47828310","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: 1
Noninvariance of weak approximation withBrauer–Manin obstruction for surfaces 具有brauer - manin障碍的曲面弱逼近的不变性
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2022-03-18 DOI: 10.4064/aa210827-19-8
Han Wu
{"title":"Noninvariance of weak approximation with\u0000Brauer–Manin obstruction for surfaces","authors":"Han Wu","doi":"10.4064/aa210827-19-8","DOIUrl":"https://doi.org/10.4064/aa210827-19-8","url":null,"abstract":". In this paper, we study the property of weak approximation with Brauer- Manin obstruction for surfaces with respect to field extensions of number fields. For any nontrivial extension of number fields L/K, assuming a conjecture of M. Stoll, we construct a smooth, projective, and geometrically connected surface over K such that it satisfies weak approximation with Brauer-Manin obstruction off all archimedean places, while its base change to L fails. Then we illustrate this construction with an explicit unconditional example.","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45257733","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
Cycle integrals of the Parson Poincaré series and intersection angles of geodesics on modular curves Parson-Poincaré级数的循环积分与模曲线上测地线的交角
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2022-03-16 DOI: 10.4064/aa220314-13-10
Alessandro Lageler, Markus Schwagenscheidt
{"title":"Cycle integrals of the Parson Poincaré series and intersection angles of geodesics on modular curves","authors":"Alessandro Lageler, Markus Schwagenscheidt","doi":"10.4064/aa220314-13-10","DOIUrl":"https://doi.org/10.4064/aa220314-13-10","url":null,"abstract":"We prove a geometric formula for the cycle integrals of Parson’s weight 2k modular integrals in terms of the intersection angles of geodesics on modular curves. Our result is an analog for modular integrals of a classical formula for the cycle integrals of certain hyperbolic Poincaré series, due to Katok. On the other hand, it extends a recent geometric formula of Matsusaka and Duke, Imamoḡlu, and Tóth for the cycle integrals of weight 2 modular integrals.","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46031524","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: 2
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