Poincaré series and zeta-function for irreducible plane curve singularities

被引：0

作者：

Stevens J. ^{[1
]}

机构：

[1] Matematik Chalmers Tekniska Högskola Och Göteborgs Universitet

来源：

Journal of Mathematical Sciences | 2007年 / 144卷 / 1期

关键词：

Complete Intersection; Euler Characteristic; Curve Singularity; Alexander Polynomial; Hypersurface Singularity;

D O I：

10.1007/s10958-007-0238-7

中图分类号：

学科分类号：

摘要：

The Poincaré series of an irreducible plane curve singularity equals the ζ-function of its monodromy, by a result of Campillo, Delgado, and Gusein-Zade. We discuss the derivation of this fact from a formula of Ebeling and Gusein-Zade relating the Poincaré series of a quasi-homogeneous complete intersection singularity to the Saito dual of a product of ζ-functions. © Springer Science+Business Media, Inc. 2007.

引用

页码：3848 / 3853

页数：5

共 50 条

[1] Poincare series and zeta function for an irreducible plane curve singularity
Stevens, J
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2005, 37 : 399 - 404
[2] ON THE ANALYTIC CLASSIFICATION OF IRREDUCIBLE PLANE CURVE SINGULARITIES
Casas-Alvero, Eduardo
[J]. ASIAN JOURNAL OF MATHEMATICS, 2021, 25 (05) : 597 - 640
[3] SOME SERIES INVOLVING THE ZETA-FUNCTION
CHOI, JS
SRIVASTAVA, HM
QUINE, JR
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1995, 51 (03) : 383 - 393
[4] TOPOLOGICAL ZETA FUNCTIONS OF COMPLEX PLANE CURVE SINGULARITIES
Le, Quy Thuong
Nguyen, Khanh Hung
[J]. OSAKA JOURNAL OF MATHEMATICS, 2023, 60 (02) : 305 - 321
[5] Dirichlet series induced by the Riemann zeta-function
Tanaka, Jun-Ichi
[J]. STUDIA MATHEMATICA, 2008, 187 (02) : 157 - 184
[6] Power series with the Riemann zeta-function in the coefficients
Katsurada, M
[J]. PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1996, 72 (03) : 61 - 63
[7] SOME SERIES INVOLVING THE RIEMANN ZETA-FUNCTION
APOSTOL, TM
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1953, 59 (05) : 449 - 450
[8] Parametrization simple irreducible plane curve singularities in arbitrary characteristic
Nguyen Hong Duc
[J]. PURE AND APPLIED MATHEMATICS QUARTERLY, 2020, 16 (04) : 1053 - 1066
[9] The Minimal Tjurina Number of Irreducible Germs of Plane Curve Singularities
Alberich-Carraminana, Maria
Almiron, Patricio
Blanco, Guillem
Melle-Hernandez, Alejandro
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2021, 70 (04) : 1211 - 1220
[10] On the monodromy of a plane curve singularity and the Poincaré series of the ring of functions on the curve
S. M. Gusein-Zade
F. Delgado
A. Campillo
[J]. Functional Analysis and Its Applications, 1999, 33 : 56 - 57

← 1 2 3 4 5 →