Quadratic Forms on F2h[T]

AbstractIn this paper, we study the representations of a polynomial in the ring F2h[T] as sums A1B1 + · · · + ArBr, or sums Y2 + A1B1 + · · · + ArBr, where Y, A1, B1, ..., Ar, Br are polynomials satisfying the most restrictive degree conditions. Such a problem is very close to the Waring problem for squares in odd characteristic. In particular, we use the Circle Method to develop asymptotic formulae for the number of representations of polynomials as sums of the above form