On \(L\)-functions of elliptic curves and anticyclotomic towers

DOI10.1007/BF01388635zbMath0565.14008OpenAlexW4250380097MaRDI QIDQ1058560

David E. Rohrlich

Publication date: 1984

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

Full work available at URL: https://eudml.org/doc/143102

zbMATH Keywords

elliptic curvegroup of rational pointscomplex multiplicationL-functionThue-Siegel-Roth theoremmaximal anticyclotomic extension

Mathematics Subject Classification ID

Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Iwasawa theory (11R23)

Related Items

The Birch and Swinnerton-Dyer Conjecture: A brief survey ⋮ Cyclotomic fields are generated by cyclotomic Hecke \(L\)-values of totally real fields ⋮ Local units, elliptic units, Heegner points and elliptic curves ⋮ Anticyclotomic Iwasawa theory of CM elliptic curves ⋮ Algebraic number theory. Abstracts from the workshop held June 25--30, 2023 ⋮ The -adic Gross–Zagier formula on Shimura curves ⋮ Effective moments of Dirichlet \(L\)-functions in Galois orbits ⋮ Ranks of Abelian varieties over infinite extensions of the rationals ⋮ On the order of vanishing of modular $L$-functions at the critical point ⋮ ON MAZUR'S CONJECTURE FOR TWISTED L-FUNCTIONS OF ELLIPTIC CURVES OVER TOTALLY REAL OR CM FIELDS ⋮ Unnamed Item ⋮ Unnamed Item ⋮ \(p\)-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin ⋮ p-adic distributions associated to Heegner points on modular curves ⋮ On the critical values of Hecke \(L\)-functions for imaginary quadratic fields ⋮ Iwasawa theory for elliptic curves over imaginary quadratic fields ⋮ \(p^{\infty}\)-Selmer groups and rational points on CM elliptic curves ⋮ On \(L\)-functions of elliptic curves and cyclotomic towers

Cites Work

• Unnamed Item
• Arithmetic on modular curves
• Congruences for special values of L-functions of elliptic curves with complex multiplication
• On the periods of modular forms
• Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer
• On the zeta-function of an abelian variety with complex multiplication
• Rational points of Abelian varieties with values in towers of number fields
• The p ‐adic generalization of the Thue‐Siegel‐Roth theorem
• The special values of the zeta functions associated with cusp forms
• ELLIPTIC CURVES OF INFINITE RANK OVER Γ-EXTENSIONS
• Rational approximations to algebraic numbers
• On the Birch and Swinnerton-Dyer conjecture

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