\(p\)-adic periods, \(p\)-adic \(L\)-functions, and the \(p\)-adic uniformization of Shimura curves.

DOI10.1215/S0012-7094-99-09809-5zbMath1037.11045OpenAlexW1667331896MaRDI QIDQ1974926

Henri Darmon, Massimo Bertolini

Publication date: 27 March 2000

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-99-09809-5

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) Arithmetic aspects of modular and Shimura varieties (11G18) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

Related Items (11)

Special values of anticyclotomic \(L\)-functions. ⋮ On the Birch and Swinnerton-Dyer conjecture for modular elliptic curves over totally real fields ⋮ Leading terms of anticyclotomic Stickelberger elements and 𝑝-adic periods ⋮ A refined Beilinson–Bloch conjecture for motives of modular forms ⋮ Shimura curves and the abc conjecture ⋮ On the derivative of anticyclotomic p-adic L-functions for Hilbert modular forms ⋮ Degrees of parametrizations of elliptic curves by Shimura curves ⋮ Proof of an exceptional zero conjecture for elliptic curves over function fields ⋮ Anticyclotomic 𝑝-adic 𝐿-functions and the exceptional zero phenomenon ⋮ On the \(p\)-adic Birch and Swinnerton-Dyer conjecture for elliptic curves over number fields ⋮ CM cycles on Shimura curves, and p-adic L-functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Values of \(p\)-adic \(L\)-functions and a \(p\)-adic Poisson kernel
• On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer
• Heegner points and derivatives of \(L\)-series
• Arithmétique des algèbres de quaternions
• Schottky groups and Mumford curves
• Coverings of p-adic symmetric regions
• p-adic automorphic functions
• Heegner points, \(p\)-adic \(L\)-functions, and the Cherednik-Drinfeld uniformization
• A proof of the Mahler-Manin conjecture
• \(p\)-adic \(L\)-functions and \(p\)-adic periods of modular forms
• Automorphic forms on GL (2)
• On construction of holomorphic cusp forms of half integral weight
• Parametrizations of elliptic curves by Shimura curves and by classical modular curves
• Heegner points on Mumford-Tate curves

This page was built for publication: \(p\)-adic periods, \(p\)-adic \(L\)-functions, and the \(p\)-adic uniformization of Shimura curves.