Multidimensional Vinogradov-type Estimates in Function Fields

Kuo, Wentang ; Liu, Yu-Ru ; Zhao, Xiaomei

Canadian journal of mathematics, Tome 66 (2014) no. 4, pp. 844-873

Résumé

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 ${{\mathbb{F}}_{q}}\left[ t \right]$ .

Détail

DOI : 10.4153/CJM-2013-014-9

Mots-clés : 16T30, 18D35, 20B30, 18D10, 20F55

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