An analogue of Kida's formula for the \(p\)-adic \(L\)-functions of modular elliptic curves

DOI10.1006/jnth.2000.2510zbMath0970.11021OpenAlexW2061106670MaRDI QIDQ1587420

Kazuo Matsuno

Publication date: 6 February 2001

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.2000.2510

zbMATH Keywords

Iwasawa invariantselliptic curve\(p\)-adic \(L\)-functionKida's formula

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Zeta functions and (L)-functions (11S40)

Related Items (5)

Iwasawa invariants for elliptic curves over \(\mathbb{Z}_p\)-extensions and Kida's formula ⋮ Consequences of the functional equation of the \(p\)-adic \(L\)-function of an elliptic curve ⋮ An analogue of Kida's formula for fine Selmer groups of elliptic curves ⋮ ON THE 2-ADIC IWASAWA INVARIANTS OF ORDINARY ELLIPTIC CURVES ⋮ The Structure of Selmer Groups of Elliptic Curves and Modular Symbols

Cites Work

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• Stickelberger elements and modular parametrizations of elliptic curves
• On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer
• L-functions and division towers
• \(\ell\)-extensions of CM-fields and cyclotomic invariants
• Arithmetic of Weil curves
• Good reduction of abelian varieties
• Congruences between Modular Forms, Cyclic Isogenies of Modular Elliptic Curves, and Integrality of 𝑝-adic 𝐿-Functions

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