The average rank of elliptic curves. I. (With an appendix by Oisín McGuinness: The explicit formula for elliptic curves over function fields)

DOI10.1007/BF01232033zbMath0783.14019WikidataQ61440673 ScholiaQ61440673MaRDI QIDQ1803375

Armand Brumer

Publication date: 29 June 1993

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/144027

zbMATH Keywords

heightHasse-Weil \(L\)-functionsBirch--Swinnerton-Dyer conjectureTaniyama-Weil conjectureaverage analytic rank of elliptic curvesranks of the Mordell-Weil groups

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Elliptic curves (14H52) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Algebraic functions and function fields in algebraic geometry (14H05)

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Cites Work

• The canonical height and integral points on elliptic curves
• Dirichlet series and automorphic forms
• L'ensemble exceptionnel dans la conjecture de Szpiro
• The behavior of the Mordell-Weil group of elliptic curves
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