Some conjectures on elliptic curves over cyclotomic fields

Dorian Goldfeld, Carlo Viola

Type: Article

Publication Date: 1983-01-01

Citations: 1

DOI: https://doi.org/10.1090/s0002-9947-1983-0688958-1

Abstract

We give conjectures for the mean values of Hasse-Weil type <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding="application/x-tex">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-functions over cyclotomic fields. In view of the Birch-Swinnerton-Dyer conjectures, this translates to interesting arithmetic information.

Locations

Transactions of the American Mathematical Society - View - PDF

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Works That Cite This (1)

Action	Title	Year	Authors
+	Eisenstein series of 1/2-integral weight and the mean value of real DirichletL-series	1985	Dorian Goldfeld Jeffrey Hoffstein

Works Cited by This (6)

Action	Title	Year	Authors
+	The arithmetic of elliptic curves	1974	John Tate
+	�ber die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen	1967	Andr� Weil
+	Mean values of L-funtions associated to elliptic, fermat and other curves at the centre of the critical strip	1979	Dorian Goldfeld Carlo Viola
+	La conjecture de Weil. I	1974	Pierre Deligne
+	Introduction to the Arithmetic Theory of Automorphic Functions	1972	Marvin Tretkoff Goro Shimura
+	Valeurs de fonctions 𝐿 et périodes d’intégrales	1979	Pierre Deligne