A generalization of Vinogradov's mean value theorem

• Autores: Scott T. Parsell
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 91, Nº 1, 2005, págs. 1-32
• Idioma: inglés
• DOI: 10.1112/s002461150501525x
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• Resumen

  • We obtain new upper bounds for the number of integral solutions of a complete system of symmetric equations, which may be viewed as a multi-dimensional version of the system considered in Vinogradov's mean value theorem. We then use these bounds to obtain Weyl-type estimates for an associated exponential sum in several variables. Finally, we apply the Hardy¿Littlewood method to obtain asymptotic formulas for the number of solutions of the Vinogradov-type system and also of a related system connected to the problem of finding linear spaces on hypersurfaces.