{"title":"On reduction maps and arithmetic dynamics of Mordell–Weil type groups","authors":"Grzegorz Banaszak, S. Baranczuk","doi":"10.4064/aa220801-17-5","DOIUrl":"https://doi.org/10.4064/aa220801-17-5","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":"70440217","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}
{"title":"$G$-bundles on the absolute Fargues–Fontaine curve","authors":"Johannes Anschütz","doi":"10.4064/aa221222-21-2","DOIUrl":"https://doi.org/10.4064/aa221222-21-2","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":"70440819","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}
Heim, Luca and Neuhauser (2019) introduced two families of polynomials in a variable $x$ generated by the arithmetic functions $g(n) = n$ and $g(n) = n^2$. They established the irreducibility over $mathbb Q$ of the family generated by $g(n) = n$ and conj
{"title":"The irreducibility of polynomials related to work of Heim, Luca and Neuhauser","authors":"Joseph C Foster, Jeremiah Southwick","doi":"10.4064/aa230212-10-7","DOIUrl":"https://doi.org/10.4064/aa230212-10-7","url":null,"abstract":"Heim, Luca and Neuhauser (2019) introduced two families of polynomials in a variable $x$ generated by the arithmetic functions $g(n) = n$ and $g(n) = n^2$. They established the irreducibility over $mathbb Q$ of the family generated by $g(n) = n$ and conj","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"24 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":"135702605","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}
We discuss a possible generalisation of a conjecture of Bley, Burns and Hahn concerning the relation between the second Adams-operator twisted Galois–Gauss sums of weakly ramified Artin characters and the square root of the inverse different of finite, od
{"title":"On Galois–Gauss sums and the square root of the inverse different","authors":"Yu Kuang","doi":"10.4064/aa220626-3-7","DOIUrl":"https://doi.org/10.4064/aa220626-3-7","url":null,"abstract":"We discuss a possible generalisation of a conjecture of Bley, Burns and Hahn concerning the relation between the second Adams-operator twisted Galois–Gauss sums of weakly ramified Artin characters and the square root of the inverse different of finite, od","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"545 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":"135912907","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}
Let $B$ be a sixth-power-free integer and $P$ be a non-torsion point on the Mordell curve $E_B:y^2=x^3+B$. We study the integral multiples $[n]P$ of $P$. Among other results, we show that $P$ has at most three integral multiples with $n gt 1$. This resul
{"title":"Multiples of integral points on Mordell curves","authors":"Amir Ghadermarzi","doi":"10.4064/aa220822-3-8","DOIUrl":"https://doi.org/10.4064/aa220822-3-8","url":null,"abstract":"Let $B$ be a sixth-power-free integer and $P$ be a non-torsion point on the Mordell curve $E_B:y^2=x^3+B$. We study the integral multiples $[n]P$ of $P$. Among other results, we show that $P$ has at most three integral multiples with $n gt 1$. This resul","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"27 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":"136372671","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}
Let $Fin mathbb Z[x,y]$ be some polynomial of degree 2. We find the asymptotic behaviour of the least common multiple of the values of $F$ up to $N$. More precisely, we consider $psi_F(N) = log(text{LCM}_{0 lt F(x,y)leq N}lbrace F(x,y) rbrace)$ a
{"title":"The least common multiple of a bivariate quadratic sequence","authors":"Noam Kimmel","doi":"10.4064/aa220719-9-7","DOIUrl":"https://doi.org/10.4064/aa220719-9-7","url":null,"abstract":"Let $Fin mathbb Z[x,y]$ be some polynomial of degree 2. We find the asymptotic behaviour of the least common multiple of the values of $F$ up to $N$. More precisely, we consider $psi_F(N) = log(text{LCM}_{0 lt F(x,y)leq N}lbrace F(x,y) rbrace)$ a","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"28 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":"135261976","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}
{"title":"A connection between uniqueness of\u0000the Riemann zeta function and the\u0000Riemann hypothesis and beyond","authors":"P. Hu, B. Li","doi":"10.4064/aa220924-9-1","DOIUrl":"https://doi.org/10.4064/aa220924-9-1","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":"70440439","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}
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