Degree bounds for modular covariants

Let V, W be representations of a cyclic group G of prime order p over a field k of characteristic p. The module of covariants k[ V, W](G) is the set of G-equivariant polynomial maps V -> W, and is a module over k[V](G) . We give a formula for the Noether bound beta(k[V, W](G), k[V](G)), i.e. the minimal degree d such that k[V, W](G) is generated over k[V](G) by elements of degree at most d.