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Multidimensional Vinogradov-type Estimates in Function Fields
Published online by Cambridge University Press: 20 November 2018
Abstract
Let ${{\mathbb{F}}_{q}}\left[ t \right]$ 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 ${{\mathbb{F}}_{q}}\left[ t \right]$. 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 ${{\mathbb{F}}_{q}}\left[ t \right]$.
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- Research Article
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- Copyright
- Copyright © Canadian Mathematical Society 2014
Footnotes
The research of the first two authors are supported by NSERC discovery grants, and the research of the third author is supported by NSFC (11126191) and NSFC(11201163). This work was completed when the third author visited the University of Waterloo in 2012, and she would like to thank the Department of Pure Mathematics for its hospitality.
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