Lattice points in elliptic paraboloids

• Autores: Fernando Chamizo Lorente , Carlos Pastor
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 63, Nº 1, 2019, págs. 343-360
• Idioma: inglés
• DOI: 10.5565/PUBLMAT6311912
• Enlaces
  • Texto completo  1    2  
• Resumen

  • We consider the lattice point problem corresponding to a family of elliptic paraboloids in Rd with d ≥ 3 and we prove the expected to be optimal exponent, improving previous results. This is especially noticeable for d = 3 because the optimal exponent is conjectural even for the sphere. We also treat some aspects of the case d = 2, getting for a simple parabolic region an Ω-result that is unknown for the classical circle and divisor problems.