Counting polynomials over finite fields with given root multiplicities

被引：0

作者：

Almousa, Ayah ^{[1
]}

Wood, Melanie Matchett ^{[1
,2
]}

机构：

[1] Univ Wisconsin, Dept Math, Madison, WI 53705 USA

[2] Amer Inst Math, Palo Alto, CA 94306 USA

来源：

JOURNAL OF NUMBER THEORY | 2014年 / 136卷

基金：

美国国家科学基金会;

关键词：

Finite fields; Configuration spaces; Square-free polynomials; CONFIGURATION-SPACES;

D O I：

10.1016/j.jnt.2013.10.015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give formulas for the number of polynomials over a finite field with given root multiplicities, in particular in cases when the formula is surprisingly simple (a power of q). Besides this concrete interpretation, we also prove an analogous result on configuration spaces in the Grothendieck ring of varieties, suggesting new homological stabilization conjectures for configuration spaces of the plane. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：394 / 402

页数：9

共 9 条

[1]

Arnold V.I., 1970, T MOSK MATEM OBVA, V21, P27

[2]

Arnold Vladimir Igorevich, 1969, MAT ZAMETKI, V5, P227

[3] Homological stability for configuration spaces of manifolds [J].

Church, Thomas .

INVENTIONES MATHEMATICAE, 2012, 188 (02) :465-504

[4]

Ellenberg Jordan, MOTIVIC PUZZLE THE M

[5]

Göttsche L, 2001, MATH RES LETT, V8, P613

[6]

Kapranov M., 2000, The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups

[7] CONFIGURATION SPACES OF POSITIVE AND NEGATIVE PARTICLES [J].

MCDUFF, D .

TOPOLOGY, 1975, 14 (01) :91-107

[8]

Randal-Williams Oscar, 2012, Q J MATH IN PRESS

[9]

Vakil Ravi, 2012, ARXIV 1208 3166

← 1 →