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A Lower Bound on the Proportion of Modular Elliptic Curves Over Galois CM Fields 伽罗瓦CM域上模椭圆曲线比例的下界
3区 数学 Q3 MATHEMATICS Pub Date : 2023-11-02 DOI: 10.1142/s1793042124500246
Zachary Feng
We calculate an explicit lower bound on the proportion of elliptic curves that are modular over any Galois CM field not containing [Formula: see text]. Applied to imaginary quadratic fields, this proportion is at least [Formula: see text]. Applied to cyclotomic fields [Formula: see text] with [Formula: see text], this proportion is at least [Formula: see text] with only finitely many exceptions of [Formula: see text], for any choice of [Formula: see text].
我们计算了在任何伽罗瓦CM域上模化的椭圆曲线比例的显式下界,不包含[公式:见文本]。应用于虚二次域,这个比例至少为[公式:见文本]。将[公式:见文]与[公式:见文]应用于切眼圈领域,这个比例至少为[公式:见文],只有[公式:见文]有有限的例外,任何[公式:见文]的选择。
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引用次数: 1
Author index (Volume 19) 作者索引(第 19 卷)
IF 0.7 3区 数学 Q3 MATHEMATICS Pub Date : 2023-11-01 DOI: 10.1142/s1793042123990014
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引用次数: 0
Computing Shintani Domains 计算新谷域
3区 数学 Q3 MATHEMATICS Pub Date : 2023-10-13 DOI: 10.1142/s1793042124500209
Alex Capunay
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引用次数: 0
Congruence properties modulo powers of 2 for overpartitions and overpartition pairs 过划分和过划分对的模幂2的同余性质
3区 数学 Q3 MATHEMATICS Pub Date : 2023-10-13 DOI: 10.1142/s1793042124500180
Dazhao Tang
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引用次数: 0
On Some Sums Involving the Integral Part Function 关于若干涉及积分部分函数的和
3区 数学 Q3 MATHEMATICS Pub Date : 2023-10-13 DOI: 10.1142/s179304212450043x
Kui Liu, Jie Wu, Zhishan Yang
Denote by $tau$ k (n), $omega$(n) and $mu$ 2 (n) the number of representations of n as product of k natural numbers, the number of distinct prime factors of n and the characteristic function of the square-free integers, respectively. Let [t] be the integral part of real number t. For f = $omega$, 2 $omega$ , $mu$ 2 , $tau$ k , we prove that n x f x n = x d 1 f (d) d(d + 1) + O $epsilon$ (x $theta$ f +$epsilon$) for x $rightarrow$ $infty$, where $theta$ $omega$ = 53 110 , $theta$ 2 $omega$ = 9 19 , $theta$ $mu$2 = 2 5 , $theta$ $tau$ k = 5k--1 10k--1 and $epsilon$ > 0 is an arbitrarily small positive number. These improve the corresponding results of Bordell{`e}s.
表示为 $tau$ K (n), $omega$(n)及 $mu$ 2 (n) n作为k个自然数乘积的表示形式的个数,n的不同质因数的个数,以及无平方整数的特征函数。设[t]为实数t的积分部分,令f = $omega$, 2 $omega$ , $mu$ 2、 $tau$ k,我们证明了n x f x n = x d1 f (d) d(d + 1) + 0 $epsilon$ (x) $theta$ F +$epsilon$) for x $rightarrow$ $infty$,其中 $theta$ $omega$ = 53 110, $theta$ 2 $omega$ = 9 19, $theta$ $mu$2 = 2 5, $theta$ $tau$ K = 5k- 1 10k- 1和 $epsilon$ > 0是一个任意小的正数。这些改进了Bordell的相应结果{è}5 .答案:
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引用次数: 11
A Dirichlet Series Related to the Error Term in the Prime Number Theorem 与素数定理中误差项有关的狄利克雷级数
3区 数学 Q3 MATHEMATICS Pub Date : 2023-10-13 DOI: 10.1142/s1793042124500362
Ertan Elma
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引用次数: 0
Hybrid Subconvexity Bounds for Twists of GL(3) L-Functions GL(3) l -函数扭转的混合子凸界
3区 数学 Q3 MATHEMATICS Pub Date : 2023-10-13 DOI: 10.1142/s1793042124500210
Xin Wang, Tengyou Zhu
Let $pi$ be a $SL(3,mathbb Z)$ Hecke-Maass cusp form and $chi$ a primitive Dirichlet character of prime power conductor $mathfrak{q}=p^k$ with $p$ prime. In this paper we will prove the following subconvexity bound $$ Lleft(frac{1}{2}+it,pitimes chiright)ll_{pi,varepsilon} p^{3/4}big(mathfrak{q}(1+|t|)big)^{3/4-3/40+varepsilon}, $$ for any $varepsilon>0$ and $t in mathbb{R}$.
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引用次数: 0
Determination of all Imaginary Cyclic Quartic Fields of Prime Class Number p ≡ 3(mod4), and non-divisibility of class numbers 素数p≡3(mod4)的所有虚循环四次域的确定,以及类数的不可除性
3区 数学 Q3 MATHEMATICS Pub Date : 2023-10-13 DOI: 10.1142/s1793042124500416
Mahesh Kumar Ram
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引用次数: 0
On 5ψ5 Identities of Bailey 关于贝利的5ψ5恒等式
3区 数学 Q3 MATHEMATICS Pub Date : 2023-10-13 DOI: 10.1142/s179304212450026x
Aritram Dhar
A BSTRACT . In this paper, we provide proofs of two 5 ψ 5 summation formulas of Bailey using a 5 φ 4 identity of Carlitz. We show that in the limiting case, the two 5 ψ 5 identities give rise to two 3 ψ 3 summation formulas of Bailey. Finally, we prove the two 3 ψ 3 identities using a technique initially used by Ismail to prove Ramanujan’s 1 ψ 1 summation formula and later by Ismail and Askey to prove Bailey’s very-well-poised 6 ψ 6 sum.
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引用次数: 0
Non-Vanishing of theta Components of Jacobi Forms with Level and an Application Jacobi型的阶分量不消失及其应用
3区 数学 Q3 MATHEMATICS Pub Date : 2023-10-13 DOI: 10.1142/s1793042124500295
Pramath Anamby
We prove that a non--zero Jacobi form of arbitrary level $N$ and square--free index $m_1m_2$ with $m_1|N$ and $(N,m_2)=1$ has a non--zero theta component $h_mu$ with either $(mu,2m_1m_2)=1$ or $(mu,2m_1m_2)nmid 2m_2$. As an application, we prove that a non--zero Siegel cusp form $F$ of degree $2$ and an odd level $N$ in the Atkin--Lehner type newspace is determined by fundamental Fourier coefficients up to a divisor of $N$.
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引用次数: 0
期刊
International Journal of Number Theory
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