Indagationes Mathematicae-New Series最新文献

英文中文

Pullback and Weil transfer on Chow groups 周组的回调和Weil转移

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-06-27 DOI: 10.1016/j.indag.2025.05.012

Nikita Karpenko, Guangzhao Zhu

In the paper “Weil transfer of algebraic cycles”, published by the first author in Indagationes Mathematicae about 25 years ago, a Weil transfer map for Chow groups of smooth algebraic varieties has been constructed and its basic properties have been established. The proof of commutativity with the pullback homomorphisms given there used a variant of Moving Lemma suffering a lack of reference. Here we are providing an alternative proof based on a more contemporary construction of the pullback via a deformation to the normal cone.

大约25年前，第一作者在《Indagationes Mathematicae》上发表了一篇题为“代数循环的Weil转移”的论文，构造了光滑代数品种Chow群的Weil转移映射，并建立了它的基本性质。这里给出的回拉同态交换性的证明使用了缺乏参考的移动引理的一种变体。在这里，我们提供了另一种证据，基于更现代的结构，通过变形到正常锥的回拉。

引用次数: 0

On the triviality of m-modified conformal vector fields 关于m-修正共形向量场的平凡性

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-06-10 DOI: 10.1016/j.indag.2025.05.009

Rahul Poddar , Ramesh Sharma

We prove that a compact Riemannian manifold

M

does not admit any non-trivial

m

-modified homothetic vector fields. In the corresponding case of an

m

-modified conformal vector field

V

, we establish an inequality that implies the triviality of

V

. Further, we demonstrate that an affine Killing

m

-modified conformal vector field on a non-compact Riemannian manifold

M

must be trivial. Finally, we show that an

m

-modified gradient conformal vector field is trivial under the assumptions of polynomial volume growth and convergence to zero at infinity.

证明了紧黎曼流形M不存在任何非平凡的M -修正齐次向量场。在相应的M -修正共形向量场V的情况下，我们建立了一个暗示V的平凡性的不等式，进一步证明了非紧黎曼流形M上的仿射杀死M -修正共形向量场一定是平凡的。最后，我们证明了在多项式体积增长和无穷远收敛于零的假设下，m修正梯度共形向量场是平凡的。

引用次数: 0

Minimal cubature rules and Koornwinder polynomials 最小培养规则和Koornwinder多项式

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-06-07 DOI: 10.1016/j.indag.2025.06.002

Yuan Xu

In his classical paper (Koornwinder, 1974), Koornwinder studied a family of orthogonal polynomials of two variables, derived from symmetric polynomials. This family possesses a rare property that orthogonal polynomials of degree

n

have

n (n + 1) / 2

real common zeros, which leads to important examples in the theory of minimal cubature rules. This paper aims to give an account of the minimal cubature rules of two variables and examples originating from Koornwinder polynomials, and we will also provide further examples.

在他的经典论文（Koornwinder, 1974）中，Koornwinder研究了由对称多项式导出的二元正交多项式族。该族具有n次正交多项式有n(n+1)/2个实数公零的罕见性质，这是最小培养规则理论中的重要例子。本文给出了两个变量的最小培养规则，并给出了源于Koornwinder多项式的例子，我们还将提供进一步的例子。

引用次数: 0

Boundary transfer matrices arising from quantum symmetric pairs 由量子对称对引起的边界转移矩阵

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-06-06 DOI: 10.1016/j.indag.2025.05.008

Andrea Appel , Bart Vlaar

We introduce a universal framework for boundary transfer matrices, inspired by Sklyanin’s two-row transfer matrix approach for quantum integrable systems with boundary conditions. The main examples arise from quantum symmetric pairs of finite and affine type. As a special case we recover a construction by Kolb in finite type. We review recent work on universal solutions to the reflection equation and highlight several open problems in this field.

受Sklyanin的具有边界条件的量子可积系统的两行转移矩阵方法的启发，我们引入了边界转移矩阵的通用框架。主要的例子来自有限型和仿射型的量子对称对。作为特例，我们恢复了有限型的Kolb构造。我们回顾了最近关于反射方程的全称解的工作，并强调了该领域的几个开放问题。

引用次数: 0

A variant of the Linnik–Sprindžuk theorem for simple zeros of Dirichlet L-functions 狄利克雷l函数的简单零点的Linnik-Sprindžuk定理的一个变体

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-06-06 DOI: 10.1016/j.indag.2025.05.007

William D. Banks

For a primitive Dirichlet character

X

, a new hypothesis

{RH}_{sim}^{†} [X]

is introduced, which asserts that (1) all simple zeros of

L (s, X)

in the critical strip are located on the critical line, and (2) these zeros satisfy some specific conditions on their vertical distribution. We show that

{RH}_{sim}^{†} [X]

(for any

X

) follows from the generalized Riemann hypothesis.

Assuming only the generalized Lindelöf hypothesis, we show that if

{RH}_{sim}^{†} [X]

holds for one primitive character

X

, then it holds for every such

X

. If this occurs, then for every character

χ

(primitive or not), all simple zeros of

L (s, χ)

in the critical strip are located on the critical line. In particular, Siegel zeros cannot exist in this situation.

对于原始Dirichlet字符X，引入了一个新的假设rsim†[X]，该假设断言(1)临界带上L（s，X）的所有简单零都位于临界线上，(2)这些零在垂直分布上满足某些特定条件。我们证明了rsim†[X]（对于任何X）都遵循广义黎曼假设。仅假设广义Lindelöf假设，我们表明，如果RHsim†[X]对一个原始字符X成立，那么它对每个这样的X都成立。如果发生这种情况，那么对于每个字符χ（原始或非原始），临界带中L（s,χ）的所有简单零都位于临界线上。特别是，在这种情况下，西格尔零不可能存在。

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引用次数: 0

Note on a sum involving the divisor function 注意一个包含除数函数的和

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-05-30 DOI: 10.1016/j.indag.2025.05.006

Liuying Wu

Let

d (n)

be the divisor function and denote by

[t]

the integral part of the real number

t

. In this paper, we prove that

\sum_{n \leq x^{1 / c}} d ((\frac{x}{n^{c}})) = d_{c} x^{1 / c} + O_{ɛ, c} (x^{max {(2 c + 2) / (2 c^{2} + 5 c + 2), 5 / (5 c + 6)} + ɛ}),

where

d_{c} = \sum_{k \geq 1} d (k) (\frac{1}{k^{1 / c}} - \frac{1}{{(k + 1)}^{1 / c}})

is a constant. This result constitutes an improvement upon that of Feng.

设d(n)为除数函数，用[t]表示实数t的积分部分。本文证明了∑n≤x1/cdxnc=dcx1/c+O /,cxmax{(2c+2)/(2c2+5c+2),5/(5c+6)}+ /，其中dc=∑k≥1d(k)1k1/c−1(k+1)1/c是一个常数。这个结果比冯的结果有了改进。

引用次数: 0

Automorphisms of the DAHA of type C1ˇC1 and non-symmetric Askey–Wilson functions C1 / C1型DAHA的自同构与非对称Askey-Wilson函数

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-05-29 DOI: 10.1016/j.indag.2025.05.005

Tom Koornwinder , Marta Mazzocco

In this paper we consider the automorphisms of the double affine Hecke algebra (DAHA) of type

\overset{ˇ}{C_{1}} C_{1}

which have a relatively simple action on the generators and on the parameters, notably a symmetry

t_{4}

which sends the Askey–Wilson (AW) parameters

(a, b, c, d)

(a, b, q d^{- 1}, q c^{- 1})

. We study how these symmetries act on the basic representation and on the symmetric and non-symmetric AW polynomials and functions. Interestingly

t_{4}

maps AW polynomials to functions. We take the rank one case of Stokman’s Cherednik kernel for

B C_{n}

as the definition of the non-symmetric Askey–Wilson function. From it we derive an expression as a sum of a symmetric and an anti-symmetric term.

在本文中，我们考虑了类型为C1 + C1的双仿射Hecke代数（DAHA）的自同构，它们对产生子和参数有相对简单的作用，特别是一个对称t4，它将Askey-Wilson （AW）参数（a,b,c,d）发送到（a,b,qd−1,qc−1）。我们研究了这些对称性如何作用于基本表示以及对称和非对称的AW多项式和函数。有趣的是，t4将AW多项式映射为函数。我们取BCn的Stokman的Cherednik核的秩一情况作为非对称Askey-Wilson函数的定义。由此我们得到一个表达式，它是一个对称项和一个反对称项的和。

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引用次数: 0

Pervasiveness of Lr(E,F) in Lr(E,Fδ) Lr（E，F）在Lr（E,Fδ）中的分布

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-05-22 DOI: 10.1016/j.indag.2025.05.003

Quinn Kiervin Starkey, Foivos Xanthos

Let

E, F

be Archimedean Riesz spaces, and let

F^{δ}

denote an order completion of

F

. In this note, we provide necessary conditions under which the space of all regular operators

L^{r} (E, F)

is pervasive in

L^{r} (E, F^{δ})

. Pervasiveness of

L^{r} (E, F)

L^{r} (E, F^{δ})

implies that the Riesz completion of

L^{r} (E, F)

can be realized as a Riesz subspace of

L^{r} (E, F^{δ})

. It also ensures that the regular part of the space of order continuous operators

L^{o c} (E, F)

forms a band of

L^{r} (E, F)

. Furthermore, the positive part

T^{+}

of any operator

T \in L^{r} (E, F)

, provided it exists, is given by the Riesz–Kantorovich formula. The results apply in particular to cases where

E = ℓ_{0}^{\infty}

E = c

, or

F

is atomic, and they provide solutions to some problems posed in Abramovich and Wickstead (1991) and Wickstead (2024).

设E，F是阿基米德Riesz空间，设Fδ表示F的一个序补全。本文给出了所有正则算子Lr（E，F）的空间在Lr（E,Fδ）中泛存的必要条件。Lr（E，F）在Lr（E,Fδ）中的普遍性意味着Lr（E，F）的Riesz补全可以通过Lr（E,Fδ）的Riesz子空间来实现。保证了阶连续算子Loc（E，F）空间的正则部分形成Lr（E，F）带。更进一步，任意算子T∈Lr（E，F）的正部T+，只要存在，则由Riesz-Kantorovich公式给出。这些结果特别适用于E= 0∞、E=c或F是原子的情况，并为Abramovich和Wickstead（1991）和Wickstead（2024）提出的一些问题提供了解决方案。

引用次数: 0

A partial-sum deformationfor a family of orthogonal polynomials 正交多项式族的部分和变形

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-05-09 DOI: 10.1016/j.indag.2025.04.007

Erik Koelink , Pablo Román , Wadim Zudilin

There are several questions one may ask about polynomials

q_{m} (x) = q_{m} (x; t) = \sum_{n = 0}^{m} t^{n} p_{n} (x)

attached to a family of orthogonal polynomials

{p_{n} (x)}_{n \geq 0}

. In this note we draw attention to the naturalness of this partial-sum deformation and related beautiful structures. In particular, we investigate the location and distribution of zeros of

q_{m} (x; t)

in the case of varying real parameter

t

对于正交多项式族{pn(x)}n≥0的多项式qm(x)=qm(x;t)=∑n=0mtnpn(x)，有几个问题。在本笔记中，我们提请注意这种部分和变形的自然性和相关的美丽结构。特别地，我们研究了在实参数t变化的情况下qm（x;t）的零点的位置和分布。

引用次数: 0

Epimorphisms between finitely generated algebras 有限生成代数之间的外胚

IF 0.8 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series

Pub Date : 2025-05-09 DOI: 10.1016/j.indag.2025.04.006

Luca Carai , Miriam Kurtzhals , Tommaso Moraschini

A quasivariety has the weak ES property when the epimorphisms between its finitely generated members are surjective. A characterization of quasivarieties with the weak ES property is obtained and a method for detecting failures of this property in quasivarieties with a near unanimity term and in congruence permutable varieties is given. It is also shown that under reasonable assumptions the weak ES property implies arithmeticity. In particular, every filtral variety with the weak ES property is a discriminator variety.

当有限生成元间的外胚是满射时，拟变具有弱ES性质。得到了一类弱ES性质的拟变簇的一个特征，并给出了在具有近一致项和同余可变簇的拟变簇中检测弱ES性质失效的方法。在合理的假设下，弱ES性质意味着算术性。特别地，每一个具有弱ES性质的滤子都是一个鉴别器。

引用次数: 0

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