On the waring rank of binary forms.

The K -rank of a binary form f in K [ x , y ] , K ⊆ C , is the smallest number of d -th powers of linear forms over K of which f is a K -linear combination. We provide lower bounds for the C -rank (Waring rank) and for the R -rank (real Waring rank) of binary forms depending on their factorization. We study binary forms with unique C -minimal representation. [ABSTRACT FROM AUTHOR]