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Multidimensional Vinogradovtype Estimates in Function Fields


Published:20130507
Printed: Aug 2014
Wentang Kuo,
Department of Pure Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, ON N2L 3G1
YuRu Liu,
Department of Pure Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, ON N2L 3G1
Xiaomei Zhao,
Department of Mathematics, Central China Normal University, Wuhan, Hubei, China 430079
Abstract
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 Vinogradovtype 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 $\mathbb{F}_q[t]$.