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UPPER BOUND FOR MONOIDAL TOPOLOGICAL COMPLEXITY 一元拓扑复杂度的上界
IF 0.4 4区 数学 Q3 MATHEMATICS Pub Date : 2020-01-01 DOI: 10.2206/kyushujm.74.197
Norio Iwase, Mitsunobu Tsutaya
. We show that tc M ( M ) ≤ 2 cat ( M ) for a finite simplicial complex M . For example, we have tc M ( S n ∨ S m ) = 2 for any positive integers n and m .
. 我们秀那油漆tc (M)≤2 (M) for afinite simplicial情结。为了操作,我们有tc (S n∨M)为任何积极integers n和M = 2。
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引用次数: 0
GAMMA FACTORS OF ZETA FUNCTIONS AS ABSOLUTE ZETA FUNCTIONS 函数的因子作为绝对函数
IF 0.4 4区 数学 Q3 MATHEMATICS Pub Date : 2020-01-01 DOI: 10.2206/kyushujm.74.441
Hidekazu Tanaka
We study the rationality of gamma factors associated to certain Hasse zeta functions. We show many explicit examples of rational gamma factors coming from products of GL(n).
我们研究了与某些Hasse zeta函数相关的gamma因子的合理性。我们给出了许多来自GL(n)乘积的有理因子的明确例子。
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引用次数: 1
CONNECTION FORMULAS RELATED WITH APPELL'S F2, HORN'S H2 AND OLSSON'S FP FUNCTIONS 与appeell的f2、horn的h2和olsson的fp函数相关的连接公式
IF 0.4 4区 数学 Q3 MATHEMATICS Pub Date : 2020-01-01 DOI: 10.2206/kyushujm.74.15
K. Mimachi
Some of the connection problems associated with the system of differential equations E2, which is satisfied by Appell’s F2 function, are solved by using integrals of Euler type. The present results give another proof of connection formulas related with Appell’s F2, Horn’s H2 and Olsson’s FP functions, which are obtained by Olsson. 0. Introduction Appell’s hypergeometric function F2 is the analytic continuation of F2(a, b1, b2, c1, c2; x, y)= ∑ m,n≥0 (a)m+n(b1)m(b2)n m!n!(c1)m(c2)n xm yn, |x | + |y|< 1, where (a)n = 0(a + n)/0(a), and satisfies the system E2 of rank four [AKdF, Er]: (E2)  [ x(1− x) ∂2 ∂x2 − xy ∂2 ∂x∂y + {c1 − (a + b1 + 1)x} ∂ ∂x − b1 y ∂ ∂y − ab1 ] F = 0, [ y(1− y) ∂2 ∂y2 − xy ∂2 ∂x∂y + {c2 − (a + b2 + 1)y} ∂ ∂y − b2x ∂ ∂x − ab2 ] F = 0, which is defined on the space C2 { {x = 0} ∪ {x = 1} ∪ {y = 0} ∪ {y = 1} ∪ {x + y = 1} } ⊂ (P1)2. In [Ol], Olsson shows that a fundamental set of solutions of E2 around the point (0, 1) in the case |x/(1− y)|< 1 or that around the point (0,∞) is given by Horn’s hypergeometric function H2 and Olsson’s hypergeometric function FP , while that around the point (0, 0) is given by F2. Moreover, he also derives some connection formulas related with F2, H2 and 2010 Mathematics Subject Classification: Primary 33C60; Secondary 33C65, 33C70.
本文用欧拉型积分法解决了由apappell的F2函数满足的微分方程组E2的一些连接问题。本文的结果再次证明了由Olsson. 0得到的与Appell 's F2、Horn 's H2和Olsson 's FP函数相关的连接公式。Appell的超几何函数F2是F2(a, b1, b2, c1, c2;x, y) =∑m, n≥0 m (a) + n (b1) m (b2) n m ! n ! (c1) m (c2) n xm yn, x y | + | | | < 1, (a) n = 0 (a + n) / 0 (a),并满足系统E2的排名四(AKdF,呃):(E2)[x(1−x)∂2∂x2−xy∂2∂x∂y + {c1−(+ b1 + 1) x}∂∂x−b1 y∂∂y−有所)F = 0, [y(1−y)∂2∂y2−xy∂2∂x∂y + {c2−(+ b2 + 1) y}∂∂y−b2x∂∂x−ab2) F = 0,这是空间上定义c2 {{x = 0}∪{x = 1}∪{y = 0}∪{y = 1}∪{x + y = 1}}⊂(P1) 2。在[Ol]中,Olsson证明了当|x/(1−y)|< 1或(0,∞)时E2绕点(0,1)的基本解集由Horn的超几何函数H2和Olsson的超几何函数FP给出,而绕点(0,0)的基本解集由F2给出。并推导出F2、H2与2010数学学科分类相关的关联公式:Primary 33C60;次级33C65, 33C70。
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引用次数: 1
PFAFFIAN SYSTEMS OF CONFLUENT HYPERGEOMETRIC FUNCTIONS OF TWO VARIABLES 两个变量的合流超几何函数的pfaffan系统
IF 0.4 4区 数学 Q3 MATHEMATICS Pub Date : 2020-01-01 DOI: 10.2206/kyushujm.74.63
Shigeo Mukai
We study Pfaffian systems of confluent hypergeometric functions of two variables with rank three, by using rational twisted cohomology groups associated with Euler-type integral representations of them. We give bases of the cohomology groups, whose intersection matrices depend only on parameters. Each connection matrix of our Pfaffian systems admits a decomposition into five parts, each of which is the product of a constant matrix and a rational 1-form on the space of variables.
利用有理扭曲上同调群及其欧拉型积分表示,研究了秩为3的两个变量合流超几何函数的Pfaffian系统。给出了交矩阵只依赖于参数的上同群的基。我们的Pfaffian系统的每一个连接矩阵都可以分解成五部分,每一部分都是一个常数矩阵与变量空间上的有理1形式的乘积。
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引用次数: 0
INTEGRAL REPRESENTATIONS OF APPELL'S F2, F3, HORN'S H2 AND OLSSON'S FP FUNCTIONS appell的f2, f3, horn的h2和olsson的fp函数的积分表示
IF 0.4 4区 数学 Q3 MATHEMATICS Pub Date : 2020-01-01 DOI: 10.2206/kyushujm.74.1
K. Mimachi
. We give integral representations of Euler type for Appell’s hypergeometric functions F 2 , F 3 , Horn’s hypergeometric function H 2 and Olsson’s hypergeometric function F P . Their integrands are the same (up to a constant factor), and only the regions of integration vary. Olsson Takayama ], and Koornwinder known that Appell’s hypergeometric function F 3 , Horn’s hypergeometric function H 2 and Olsson’s hypergeometric function P also appear as solutions of . Here Appell’s F 3 , Horn’s H 2 and Olsson’s F P are analytic
. 给出了Appell的超几何函数f2、f3、Horn的超几何函数h2和Olsson的超几何函数fp的欧拉型积分表示。它们的积分是相同的(直到一个常数因子),只是积分的区域不同。Olsson Takayama],和Koornwinder知道apell的超几何函数f3、Horn的超几何函数h2和Olsson的超几何函数P也作为的解出现。这里,阿佩尔的f3,霍恩的h2和奥尔森的fp是解析的
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引用次数: 2
ON PROPER HOLOMORPHIC MAPPINGS BETWEEN TWO EQUIDIMENSIONAL FBH-TYPE DOMAINS 两个等维fbh型域间的真全纯映射
IF 0.4 4区 数学 Q3 MATHEMATICS Pub Date : 2020-01-01 DOI: 10.2206/kyushujm.74.149
A. Kodama
We introduce a new class of domains Dn,m(μ, p), called FBH-type domains, in Cn × Cm , where 0< μ ∈ R and p ∈ N. In the special case of p = 1, these domains are just the Fock–Bargmann–Hartogs domains Dn,m(μ) in Cn × Cm introduced by Yamamori. In this paper we obtain a complete description of an arbitrarily given proper holomorphic mapping between two equidimensional FBH-type domains. In particular, we prove that the holomorphic automorphism group Aut(Dn,m(μ, p)) of any FBH-type domain Dn,m(μ, p) with p 6= 1 is a Lie group isomorphic to the compact connected Lie group U (n)×U (m). This tells us that the structure of Aut(Dn,m(μ, p)) with p 6= 1 is essentially different from that of Aut(Dn,m(μ)).
我们在Cn × Cm中引入了一类新的域Dn,m(μ, p),称为fbh型域,其中0< μ∈R, p∈n。在p = 1的特殊情况下,这些域正是Yamamori在Cn × Cm中引入的Fock-Bargmann-Hartogs域Dn,m(μ)。本文给出了两个等维fbh型域之间任意给定的固有全纯映射的完整描述。特别地,我们证明了任意fbh型定义域Dn,m(μ, p)且p 6= 1的全纯自同构群Aut(Dn,m(μ, p))是紧连通李群U (n)×U (m)同构的李群,这说明了当p 6= 1时Aut(Dn,m(μ, p))的结构与Aut(Dn,m(μ))的结构本质上是不同的。
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引用次数: 0
ON EXTREMAL QUASI-MODULAR FORMS AFTER KANEKO AND KOIKE 在kaneko和koike之后的极值拟模形式
IF 0.4 4区 数学 Q3 MATHEMATICS Pub Date : 2019-10-25 DOI: 10.2206/kyushujm.74.401
F. Pellarin, G. Nebe
Kaneko and Koike introduced the notion of extremal quasi-modular form and proposed conjectures on their arithmetic properties. The aim of this note is to prove a rather sharp multiplicity estimate for these quasi-modular forms. The note ends with discussions and partial answers around these conjectures and an appendix by G. Nebe containing the proof of the integrality of the Fourier coefficients of the normalised extremal quasimodular form of weight 14 and depth 1.
Kaneko和Koike引入了极值拟模形式的概念,并对其算术性质提出了猜想。本文的目的是证明这些准模形式的一个相当尖锐的重性估计。笔记以围绕这些猜想的讨论和部分答案结束,G. Nebe的附录包含了权值14和深度1的归一化极值拟模形式的傅里叶系数的完整性证明。
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引用次数: 8
ON THE PARITY RESULT FOR MULTIPLE DIRICHLET SERIES 关于多重DIRICHLET级数的奇偶性结果
IF 0.4 4区 数学 Q3 MATHEMATICS Pub Date : 2019-09-13 DOI: 10.2206/kyushujm.76.1
Shin-ya Kadota
In this paper, we discuss the parity result for multiple Dirichlet series which contains some special values of multiple zeta functions as special cases, Mordell--Tornheim type of multiple zeta values, zeta values of the root systems and so on. Moreover, we can give explicit expression in terms of lower series by using main theorem.
本文讨论了包含多个zeta函数的某些特殊值的多重Dirichlet级数的奇偶性结果,作为特例,讨论了多重zeta值的Mordell—Tornheim型,根的zeta值等。并利用主要定理给出了下级数的显式表达式。
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引用次数: 0
PRINCIPAL FACTORS AND LATTICE MINIMA IN CUBIC FIELDS 三次域中的主因子与格极小
IF 0.4 4区 数学 Q3 MATHEMATICS Pub Date : 2019-07-22 DOI: 10.2206/kyushujm.76.101
S. Aouissi, A. Azizi, M. C. Ismaili, D. C. Mayer, M. Talbi
Let $mathit{k}=mathbb{Q}(sqrt[3]{d},zeta_3)$, where $d>1$ is a cube-free positive integer, $mathit{k}_0=mathbb{Q}(zeta_3)$ be the cyclotomic field containing a primitive cube root of unity $zeta_3$, and $G=operatorname{Gal}(mathit{k}/mathit{k}_0)$. The possible prime factorizations of $d$ in our main result [2, Thm. 1.1] give rise to new phenomena concerning the chain $Theta=(theta_i)_{iinmathbb{Z}}$ of textit{lattice minima} in the underlying pure cubic subfield $L=mathbb{Q}(sqrt[3]{d})$ of $mathit{k}$. The aims of the present work are to give criteria for the occurrence of generators of primitive ambiguous principal ideals $(alpha)inmathcal{P}_{mathit{k}}^G/mathcal{P}_{mathit{k}_0}$ among the lattice minima $Theta=(theta_i)_{iinmathbb{Z}}$ of the underlying pure cubic field $L=mathbb{Q}(sqrt[3]{d})$, and to explain exceptional behavior of the chain $Theta$ for certain radicands $d$ with impact on determining the principal factorization type of $L$ and $mathit{k}$ by means of Voronoi's algorithm.
设$mathit{k}=mathbb{Q}(sqrt[3]{d},zeta_3)$,其中$d>1$是一个无立方体的正整数,$mathi{k}_0=mathbb{Q}(zeta_3)$是包含单位原始立方根$zeta_3$的分圆域,$G=operatorname{Gal}(mathit{k}/mathit{k}_0)$。在我们的主要结果[2,Thm.1.1]中$d$的可能素数因子分解引起了关于$mathit{k}$的底层纯三次子域$L=mathbb{Q}(sqrt[3]{d})$中textit{lattice minimum}的链$Theta=(Theta_i)_。本工作的目的是给出原始模糊主理想$(alpha)inmathcal的生成元出现的标准{P}_{mathit{k}}^G/mathcal{P}_{mathit{k}_0}$在底层纯三次域$L=mathbb{Q}(sqrt[3]{d})$的格极小值$Theta=。
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引用次数: 1
MULTIPLE ZETA VALUES AND ITERATED LOG-SINE INTEGRALS 多重ζ值与迭代LOG-SINE积分
IF 0.4 4区 数学 Q3 MATHEMATICS Pub Date : 2019-04-22 DOI: 10.2206/kyushujm.74.233
Ryo Umezawa
We introduce an iterated integral version of (generalized) log-sine integrals (iterated log-sine integrals) and prove a relation between a multiple polylogarithm and iterated log-sine integrals. We also give a new method for obtaining relations among multiple zeta values, which uses iterated log-sine integrals, and give alternative proofs of several known results related to multiple zeta values and log-sine integrals.
我们引入了(广义)对数正弦积分(迭代对数正弦积分)的迭代积分版本,并证明了多重多对数与迭代对数正弦积之间的关系。我们还给出了一种利用迭代对数正弦积分获得多个ζ值之间关系的新方法,并给出了与多个ζ值和对数正弦积分有关的几个已知结果的替代证明。
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引用次数: 2
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Kyushu Journal of Mathematics
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