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1. CJM 2013 (vol 66 pp. 844)

Kuo, Wentang; Liu, Yu-Ru; Zhao, Xiaomei
 Multidimensional Vinogradov-type Estimates in Function Fields Let \$\mathbb{F}_q[t]\$ denote the polynomial ring over the finite field \$\mathbb{F}_q\$. We employ Wooley's new efficient congruencing method to prove certain multidimensional Vinogradov-type estimates in \$\mathbb{F}_q[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 \$\mathbb{F}_q[t]\$. Keywords:Vinogradov's mean value theorem, function fields, circle methodCategories:11D45, 11P55, 11T55