Ragot, Jean-François Counting polynomials with zeros of given multiplicities in finite fields. (English) Zbl 1024.11076 Finite Fields Appl. 5, No. 3, 219-231, Art. ffta.1999.0244 (1999). Summary: We consider the set of polynomials in \(r\) indeterminates over a finite field and with bounded degree. We give here a way to count the number of elements of some of its subsets, namely those sets defined by the multiplicities of their elements at some points of \(\mathbb{F}^r_q\). The number of polynomials having at least one zero in a given finite field is computed as a particular applications. Cited in 2 Documents MSC: 11T06 Polynomials over finite fields Keywords:polynomials; finite field PDFBibTeX XMLCite \textit{J.-F. Ragot}, Finite Fields Appl. 5, No. 3, 219--231 (1999; Zbl 1024.11076) Full Text: DOI