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Multidimensional Vinogradov-type Estimates in Function Fields

  Published:2013-05-07
 Printed: Aug 2014
  • Wentang Kuo,
    Department of Pure Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, ON N2L 3G1
  • Yu-Ru 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
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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 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 method Vinogradov's mean value theorem, function fields, circle method
MSC Classifications: 11D45, 11P55, 11T55 show english descriptions Counting solutions of Diophantine equations
Applications of the Hardy-Littlewood method [See also 11D85]
Arithmetic theory of polynomial rings over finite fields
11D45 - Counting solutions of Diophantine equations
11P55 - Applications of the Hardy-Littlewood method [See also 11D85]
11T55 - Arithmetic theory of polynomial rings over finite fields
 

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