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Acta Arithmetica最新文献

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On $d$-complete sequences of integers, II 在$d$-整数完全序列上，II
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2023-01-01 DOI: 10.4064/aa220818-20-1
Yong-Gao Chen, Wang Yu
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引用次数: 0
Powers from products of terms in progressions with gaps 幂由带间隙的级数项的乘积得到
3区 数学
Acta Arithmetica Pub Date : 2023-01-01 DOI: 10.4064/aa220811-13-9
Michael A. Bennett
{"title":"Powers from products of terms in progressions with gaps","authors":"Michael A. Bennett","doi":"10.4064/aa220811-13-9","DOIUrl":"https://doi.org/10.4064/aa220811-13-9","url":null,"abstract":"","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134884236","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
Certain Diophantine equations and new parity results for 21-regular partitions 21正则分区的某些Diophantine方程和新的宇称结果
3区 数学
Acta Arithmetica Pub Date : 2023-01-01 DOI: 10.4064/aa230203-5-7
Ajit Singh, Gurinder Singh, Rupam Barman
{"title":"Certain Diophantine equations and new parity results for 21-regular partitions","authors":"Ajit Singh, Gurinder Singh, Rupam Barman","doi":"10.4064/aa230203-5-7","DOIUrl":"https://doi.org/10.4064/aa230203-5-7","url":null,"abstract":"For a positive integer $tgeq 2$, let $b_{t}(n)$ denote the number of $t$-regular partitions of a non-negative integer $n$. In a recent paper, Keith and Zanello (2022) investigated the parity of $b_{t}(n)$ when $tleq 28$. They discovered new infinite fam","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"242 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135440483","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 cubic Pell equation $L$-function 三次佩尔方程L函数
3区 数学
Acta Arithmetica Pub Date : 2023-01-01 DOI: 10.4064/aa220918-18-8
Dorian Goldfeld, Gerhardt Hinkle
{"title":"The cubic Pell equation $L$-function","authors":"Dorian Goldfeld, Gerhardt Hinkle","doi":"10.4064/aa220918-18-8","DOIUrl":"https://doi.org/10.4064/aa220918-18-8","url":null,"abstract":"For $d gt 1$ a cubefree rational integer, we define an $L$-function (denoted $L_d(s)$) whose coefficients are derived from the cubic theta function for $mathbb Q(sqrt {-3})$. The Dirichlet series defining $L_d(s)$ converges for ${rm Re}(s) gt 1$, and","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135839483","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
A Bombieri–Vinogradov-type theorem for moduli with small radical 具有小根模的bombieri - vinogradov型定理
3区 数学
Acta Arithmetica Pub Date : 2023-01-01 DOI: 10.4064/aa221211-1-9
Stephan Baier, Sudhir Pujahari
{"title":"A Bombieri–Vinogradov-type theorem for moduli with small radical","authors":"Stephan Baier, Sudhir Pujahari","doi":"10.4064/aa221211-1-9","DOIUrl":"https://doi.org/10.4064/aa221211-1-9","url":null,"abstract":"In this article, we extend our recent work on a Bombieri–Vinogradov-type theorem for sparse sets of prime powers $p^Nleqslant x^{1/4-varepsilon }$ with $pleqslant (log x)^C$ to sparse sets of moduli $sleqslant x^{1/3-varepsilon }$ with radical rad$(","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135263345","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
$varOmega$-result for the remainder term in Beurling’s prime number theorem for well-behaved integers $varOmega$-对表现良好的整数的伯林素数定理的余数项的结果
IF 0.7 3区 数学
Acta Arithmetica Pub Date : 2023-01-01 DOI: 10.4064/aa220516-20-3
T. Hilberdink, Laima Kaziulytė
{"title":"$varOmega$-result for the remainder term in Beurling’s prime number theorem for well-behaved integers","authors":"T. Hilberdink, Laima Kaziulytė","doi":"10.4064/aa220516-20-3","DOIUrl":"https://doi.org/10.4064/aa220516-20-3","url":null,"abstract":"","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70440102","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 orders in quadratic number fields with unusual sets of distances 在具有不寻常距离集的二次数域中的阶
3区 数学
Acta Arithmetica Pub Date : 2023-01-01 DOI: 10.4064/aa230515-4-10
Andreas Reinhart
{"title":"On orders in quadratic number fields with unusual sets of distances","authors":"Andreas Reinhart","doi":"10.4064/aa230515-4-10","DOIUrl":"https://doi.org/10.4064/aa230515-4-10","url":null,"abstract":"Let $mathcal O$ be an order in an algebraic number field and suppose that the set of distances $varDelta (mathcal O)$ of $mathcal O$ is nonempty (equivalently, $mathcal O$ is not half-factorial). If $mathcal O$ is seminormal (in particular, if $mat","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135261686","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
Corrigendum to “Explicit estimates for the summatory function of ${{varLambda }}(n)/n$ from the one of ${{varLambda }}(n)$” (Acta Arith. 159 (2013), 113–122) 对 "从 ${{varLambda }}(n)$ 的求和函数对 ${{varLambda }}(n)$ 的求和函数的显式估计 "的更正 (Acta Arith.159 (2013), 113-122)
3区 数学
Acta Arithmetica Pub Date : 2023-01-01 DOI: 10.4064/aa220605-11-10
Olivier Ramaré
{"title":"Corrigendum to “Explicit estimates for the summatory function of ${{varLambda }}(n)/n$ from the one of ${{varLambda }}(n)$” (Acta Arith. 159 (2013), 113–122)","authors":"Olivier Ramaré","doi":"10.4064/aa220605-11-10","DOIUrl":"https://doi.org/10.4064/aa220605-11-10","url":null,"abstract":"","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135318029","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
Diophantine approximation and primitive prime divisors in random iterations 丢番图近似和随机迭代中的原始素数
3区 数学
Acta Arithmetica Pub Date : 2023-01-01 DOI: 10.4064/aa230303-12-8
Ruofan Li
{"title":"Diophantine approximation and primitive prime divisors in random iterations","authors":"Ruofan Li","doi":"10.4064/aa230303-12-8","DOIUrl":"https://doi.org/10.4064/aa230303-12-8","url":null,"abstract":"We show that, under some mild conditions, the orbit of an algebraic number under random iterations cannot approach another algebraic number very fast. As an application of this result, we prove that, in certain cases, all but finitely many terms in such a","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135704395","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
Quaternary quadratic forms with prime discriminant 具有素数判别式的四元二次型
3区 数学
Acta Arithmetica Pub Date : 2023-01-01 DOI: 10.4064/aa220601-14-7
Jeremy Rouse, Katherine Thompson
{"title":"Quaternary quadratic forms with prime discriminant","authors":"Jeremy Rouse, Katherine Thompson","doi":"10.4064/aa220601-14-7","DOIUrl":"https://doi.org/10.4064/aa220601-14-7","url":null,"abstract":"Let $Q$ be a positive-definite quaternary quadratic form with prime discriminant. We give an explicit lower bound on the number of representations of a positive integer $n$ by $Q$. This problem is connected with deriving an upper bound on the Petersson no","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009415","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
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