Multidimensional Vinogradov-type Estimates in Function Fields
Wentang Kuo, Yuru Liu, Xiaomei Zhao · Canadian Journal of Mathematics · 2013
Abstract Let 𝔽q[t] denote the polynomial ring over the finite field 𝔽q. We 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].