On the number of zeros of multiplicity r

Hans Olav Geil, Casper Thomsen

Publikation: AndetUdgivelser på nettet - Net-publikationForskning


Let S be a finite subset of a field. For multivariate polynomials the generalized Schwartz-Zippel bound [2], [4] estimates the number of zeros over Sx...xS counted with multiplicity. It does this in terms of the total degree, the number of variables and |S|. In the present work we take into account what is the leading monomial. This allows us to consider more general point ensembles and most importantly it allows us to produce much more detailed information about the number of zeros of multiplicity r than can be deduced from the generalized Schwartz-Zippel bound. We present both upper and lower bounds.
Publikationsdato8 dec. 2009
StatusUdgivet - 8 dec. 2009

Bibliografisk note

Senest ændret: 21/12/2009


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