The Computational and Theoretical Aspects of Elliptic Curves
Description
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 Computational Aspects of the Birch and Swinnerton-Dyer Conjecture". The first was held at Beijing International Centre for Mathematical Research (BICMR) in December 2014 and the second was held at the International Centre for Theoretical Sciences (ICTS), Bangalore, India in December 2016. Providing a broad overview of the subject, the book is a valuable resource for young researchers wishing to work in this area. The articles have an extensive list of references to enable diligent researchers to gain an idea of the current state of art on this conjecture.
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Content
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