Multidimensional Vinogradov-type Estimates in Function Fields

Abstract. Let Fq[t] be the ring of polynomials over the finite field Fq. In this talk, we will employ Wooley’s new efficient congruencing method to prove certain multidimensional Vinogradov-type estimates in Fq[t]. These results allow us to apply a variant of the circle method to obtain asymptotic formulas for a system connected to the problem about linear spaces lying on hypersurfaces defined over Fq[t]. This is a joint work with Wentang Kuo and Xiaomei Zhao.