Counting polynomials over finite fields with given root multiplicities

JOURNAL OF NUMBER THEORY

卷:136

Article

Almousa, Ayah¹  Wood, Melanie Matchett^1,2 

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

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

关键词: Finite fields;    Configuration spaces;    Square-free polynomials;   

DOI  :  10.1016/j.jnt.2013.10.015

来源: Elsevier

【 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.

【 授权许可】

Free