FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI最新文献

A uniform semi-local limit theorem along sets of multiples for sums of i.i.d. random variables 沿 i.i.d. 随机变量之和的倍数集的均匀半局部极限定理

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FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2024-01-01 DOI: 10.7169/facm/2078

Michel J.G. Weber

引用次数: 0

On the class numbers of the $n$-th layers in the cyclotomic $mathbb{Z}_2$-extension of $mathbb{Q}(sqrt{5})$ 关于 $mathbb{Q}(sqrt{5})$ 的环状 $n$ 层的类数

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FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2024-01-01 DOI: 10.7169/facm/2058

Takuya Aoki

引用次数: 0

On the monogenicity of power-compositional Shanks polynomials 幂-复合Shanks多项式的单性性

FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2023-09-15 DOI: 10.7169/facm/2104

Lenny Jones

{"title":"On the monogenicity of power-compositional Shanks polynomials","authors":"Lenny Jones","doi":"10.7169/facm/2104","DOIUrl":"https://doi.org/10.7169/facm/2104","url":null,"abstract":"Let $f(x)in mathbb{Z}[x]$ be a monic polynomial of degree $N$ that is irreducible over $mathbb{Q}$. We say $f(x)$ is emph{monogenic} if $Theta={1,theta,theta^2,ldots ,theta^{N-1}}$ is a basis for the ring of integers $mathbb{Z}_K$ of $K=mathbb{Q}(theta)$, where $f(theta)=0$. If $Theta$ is not a basis for $mathbb{Z}_K$, we say that $f(x)$ is emph{non-monogenic}.Let $kge 1$ be an integer, and let $(U_n)$be the sequence defined by [U_0=U_1=0,qquad U_2=1 qquad text{and}qquad U_n=kU_{n-1}+(k+3)U_{n-2}+U_{n-3} qquad text{for $nge 3$}.] It is well known that $(U_n)$ is periodic modulo any integer $mge 2$, and we let $pi(m)$ denote the length of this period. We define a emph{$k$-Shanks prime} to be a prime $p$ such that $pi(p^2)=pi(p)$. Let $mathcal{S}_k(x)=x^{3}-kx^{2}-(k+3)x-1$ and $mathcal{D}=(k^2+3k+9)/gcd(3,k)^2$. Suppose that $knot equiv 3 pmod{9}$ and that $mathcal{D}$ is squarefree. In this article, we prove that $p$ is a $k$-Shanks prime if and only if $mathcal{S}_k(x^p)$ is non-monogenic, for any prime $p$ such that $mathcal{S}_k(x)$ is irreducible in $mathbb{F}_p[x]$. Furthermore, we show that $mathcal{S}_k(x^p)$ is monogenic for any prime divisor $p$ of $mathcal{D}$. These results extend previous work of the author on $k$-Wall-Sun-Sun primes.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135394108","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: 1

Moments of Gaussian hypergeometric functions over finite fields 有限域上高斯超几何函数的矩

FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2023-09-15 DOI: 10.7169/facm/2088

Ankan Pal, Bidisha Roy, Mohammad Sadek

引用次数: 0

On the arithmetic of polynomials with coefficients in Mordell-Weil type groups modell - weil型群中带系数多项式的算法

FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2023-09-15 DOI: 10.7169/facm/2105

Stefan Barańczuk

引用次数: 0

Polynomials realizing images of Galois representations of an elliptic curve 实现椭圆曲线图像伽罗瓦表示的多项式

FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2023-09-15 DOI: 10.7169/facm/2106

Zoé Yvon

引用次数: 0

The variation of general Fourier coefficients 一般傅立叶系数的变化

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FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2023-01-01 DOI: 10.7169/facm/2002

V. Tsagareishvili

引用次数: 0

Bounding the number of lattice pointsnear a convex curve by curvature 用曲率限定凸曲线附近的点阵数目

FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2023-01-01 DOI: 10.7169/facm/2087

Ralph Howard, Ognian Trifonov

引用次数: 1

Bounds for the smallest integral solutionof Pell equation over a number field Pell方程在数域上的最小积分解的界

FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2023-01-01 DOI: 10.7169/facm/2095

Paraskevas Alvanos, Dimitrios Poulakis

引用次数: 0

Coefficient bound associated with certain Hankel determinants and Zalcman conjecturefor a subfamily of multivalent bounded turning functions 多价有界翻转函数亚族与某些Hankel行列式相关的系数界和Zalcman猜想

FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2023-01-01 DOI: 10.7169/facm/2076

N. Vani, D. Vamshee Krishna, Ch. Vijaya Kumar, B. Rath, K. Sanjay Kumar

引用次数: 0