The number of extensions of a number field with fixed degree and bounded discriminant

• Autores: Akshay Venkatesh, Jordan S. Ellenberg
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 163, Nº 2, 2006, págs. 723-741
• Idioma: inglés
• DOI: 10.4007/annals.2006.163.723
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• Resumen

  • We give an upper bound on the number of extensions of a fixed number field of prescribed degree and discriminant ¡Ü X; these bounds improve on work of Schmidt. We also prove various related results, such as lower bounds for the number of extensions and upper bounds for Galois extensions.