On Waring's problem for several algebraic forms

  • Enrico Carlini

    Monash University, Clayton, Australia
  • Jaydeep V. Chipalkatti

    University of British Columbia, Vancouver, Canada


We reconsider the classical problem of representing a finite number of forms of degree d in the polynomial ring over n + 1 variables as scalar combinations of powers of linear forms. We define a geometric construct called a 'grove', which, in a number of cases, allows us to determine the dimension of the space of forms which can be so represented for a fixed number of summands. We also present two new examples, where this dimension turns out to be less than what a naïve parameter count would predict.

Cite this article

Enrico Carlini, Jaydeep V. Chipalkatti, On Waring's problem for several algebraic forms. Comment. Math. Helv. 78 (2003), no. 3, pp. 494–517

DOI 10.1007/S00014-003-0769-6