The Computational and Theoretical Aspects of Elliptic Curves

• Corporate Author: SpringerLink (Online service)
• Other Authors: Liang, Zhibin (Editor, http://id.loc.gov/vocabulary/relators/edt), Aribam, Chandrakant (Editor, http://id.loc.gov/vocabulary/relators/edt)
• Format: Electronic eBook
• Language: English
• Published: Singapore : Springer Singapore : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Mathematical Lectures from Peking University,
• Subjects: Number theory.; Algebraic geometry.; Number Theory.; Algebraic Geometry.

This volume presents a collection of results related to the BSD conjecture, based on the first two India-China conferences on this topic. It provides an overview of the conjecture and a few special cases where the conjecture is proved. The broad theme of the two conferences was "Theoretical and...

Table of Contents:

• Introduction to the Conjectures of Birch and Swinnerton-Dyer
• Kolyvagin's Work on Modular Elliptic Curves
• p-Adic Analogues of The BSD Conjecture and the L-invariant
• Quadratic Twists of Elliptic Curves
• Computing Fourier Coefficients of Level One Modular Forms
• Hecke Algebras, New Vectors and New Spaces
• A Note on a Formula of Special Values of Dirichlet L-Functions
• On Orders of Tame Kernels In Quaternion Extension of Number Fields.