International Journal of Number Theory最新文献_第8页

Intermediate modular curves with infinitely many cubic points over ℚ 具有无穷多个三次点的中间模曲线

3区数学

International Journal of Number Theory Pub Date : 2023-10-13 DOI: 10.1142/s1793042124500350

Tarun Dalal

引用次数: 0

On some discrete mean values of higher derivatives of Hardy's Z-Function 哈迪z函数高阶导数的离散均值

3区数学

International Journal of Number Theory Pub Date : 2023-10-13 DOI: 10.1142/s1793042124500325

Hirotaka Kobayashi

引用次数: 0

Determination of normalized extremal quasimodular forms of depth 1 with integral Fourier coefficients 用积分傅立叶系数确定深度1的归一化极值拟模形式

3区数学

International Journal of Number Theory Pub Date : 2023-10-13 DOI: 10.1142/s1793042124500337

Tomoaki Nakaya

引用次数: 1

On The X-Coordinates of Pell Equations X2 − dY2 = ±1 As Difference of two Fibonacci Numbers 关于Pell方程的x坐标X2−dY2 =±1作为两个Fibonacci数的差

3区数学

International Journal of Number Theory Pub Date : 2023-10-13 DOI: 10.1142/s1793042124500258

Carlos A. Gomez, Salah Eddine Rihane, Alain Togbe

引用次数: 0

A Two-Parametric Family of High Rank Mordell Curves 高阶莫德尔曲线的两参数族

3区数学

International Journal of Number Theory Pub Date : 2023-10-13 DOI: 10.1142/s1793042124500428

Mikhail A. Reynya

引用次数: 0

Primes in denominators of algebraic numbers 代数数分母中的质数

3区数学

International Journal of Number Theory Pub Date : 2023-10-13 DOI: 10.1142/s1793042124500167

Deepesh Singhal, Yuxin Lin

{"title":"Primes in denominators of algebraic numbers","authors":"Deepesh Singhal, Yuxin Lin","doi":"10.1142/s1793042124500167","DOIUrl":"https://doi.org/10.1142/s1793042124500167","url":null,"abstract":"Denote the set of algebraic numbers as $overline{mathbb{Q}}$ and the set of algebraic integers as $overline{mathbb{Z}}$. For $gammainoverline{mathbb{Q}}$, consider its irreducible polynomial in $mathbb{Z}[x]$, $F_{gamma}(x)=a_nx^n+dots+a_0$. Denote $e(gamma)=gcd(a_{n},a_{n-1},dots,a_1)$. Drungilas, Dubickas and Jankauskas show in a recent paper that $mathbb{Z}[gamma]cap mathbb{Q}={alphainmathbb{Q}mid {pmid v_p(alpha)<0}subseteq {pmid p|e(gamma)}}$. Given a number field $K$ and $gammainoverline{mathbb{Q}}$, we show that there is a subset $X(K,gamma)subseteq text{Spec}(mathcal{O}_K)$, for which $mathcal{O}_K[gamma]cap K={alphain Kmid {mathfrak{p}mid v_{mathfrak{p}}(alpha)<0}subseteq X(K,gamma)}$. We prove that $mathcal{O}_K[gamma]cap K$ is a principal ideal domain if and only if the primes in $X(K,gamma)$ generate the class group of $mathcal{O}_K$. We show that given $gammain overline{mathbb{Q}}$, we can find a finite set $Ssubseteq overline{mathbb{Z}}$, such that for every number field $K$, we have $X(K,gamma)={mathfrak{p}intext{Spec}(mathcal{O}_K)mid mathfrak{p}cap Sneq emptyset}$. We study how this set $S$ relates to the ring $overline{mathbb{Z}}[gamma]$ and the ideal $mathfrak{D}_{gamma}={ainoverline{mathbb{Z}}mid agammainoverline{mathbb{Z}}}$ of $overline{mathbb{Z}}$. We also show that $gamma_1,gamma_2in overline{mathbb{Q}}$ satisfy $mathfrak{D}_{gamma_1}=mathfrak{D}_{gamma_2}$ if and only if $X(K,gamma_1)=X(K,gamma_2)$ for all number fields $K$.","PeriodicalId":14293,"journal":{"name":"International Journal of Number Theory","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135918316","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

Log-Concavity of Infinite Product and Infinite Sum Generating Functions 无穷积与无穷和生成函数的对数凹性

3区数学

International Journal of Number Theory Pub Date : 2023-10-13 DOI: 10.1142/s1793042124500192

Bernhard Heim, Markus Neuhauser

{"title":"Log-Concavity of Infinite Product and Infinite Sum Generating Functions","authors":"Bernhard Heim, Markus Neuhauser","doi":"10.1142/s1793042124500192","DOIUrl":"https://doi.org/10.1142/s1793042124500192","url":null,"abstract":"We expand on the remark by Andrews on the importance of infinite sums and products in combinatorics. Let ${g_d(n)}_{dgeq 0,n geq 1}$ be the double sequences $sigma_d(n)= sum_{ell mid n} ell^d$ or $psi_d(n)= n^d$. We associate double sequences $left{ p^{g_{d} }left( nright) right}$ and $left{ q^{g_{d} }left( nright) right} $, defined as the coefficients of begin{eqnarray*} sum_{n=0}^{infty} p^{g_{d} }left( nright) , t^{n}&:=&prod_{n=1}^{infty} left( 1 - t^{n} right)^{-frac{ sum_{ell mid n} mu(ell) , g_d(n/ell) }{n} }, sum_{n=0}^{infty} q^{g_{d} }left( nright) , t^{n}&:=&frac{1}{1 - sum_{n=1}^{infty} g_d(n) , t^{n} }. end{eqnarray*} These coefficients are related to the number of partitions $mathrm{p}left( nright) = p^{sigma _{1 }}left ( nright) $, plane partitions $ppleft( nright) = p^{sigma _{2 }}left( nright) $ of $n$, and Fibonacci numbers $F_{2n} = q^{psi _{1 }}left( nright) $. Let $n geq 3$ and let $n equiv 0 pmod{3}$. Then the coefficients are log-concave at $n$ for almost all $d$ in the exponential and geometric cases. The coefficients are not log-concave for almost all $d$ in both cases, if $n equiv 2 pmod{3}$. Let $nequiv 1 pmod{3}$. Then the log-concave property flips for almost all $d$.","PeriodicalId":14293,"journal":{"name":"International Journal of Number Theory","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135918468","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

Iwasawa theory of plus/minus Selmer groups with non-co-free plus/minus local conditions 非共自由正/负局域条件下的正/负Selmer群的Iwasawa理论

3区数学

International Journal of Number Theory Pub Date : 2023-10-13 DOI: 10.1142/s1793042124500386

Byoung Du Kim

引用次数: 0

Interlacing Properties for Zeros of a Family of Modular Forms 一类模形式的零的交错性质

3区数学

International Journal of Number Theory Pub Date : 2023-10-13 DOI: 10.1142/s1793042124500222

William Frendreiss, Jennifer Gao, Austin Lei, Amy Woodall, Hui Xue, Daozhou Zhu

引用次数: 0

The mahler measure of x + 1/x + y + 1/y + 4 ± 42 and Beilinson’s conjecture 马勒测量x + 1/x + y + 1/y + 4±42和贝林森猜想