Advanced Topics in the Arithmetic of Elliptic Curves pdf epub mobi txt 电子书下载 2024

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Joseph H. Silverman

Springer

1999-09-24

538

USD 54.95

Paperback

Graduate Texts in Mathematics

9780387943282

图书标签: 数论数学 elliptic_curves elliptic curves 解析数论7 Number_Theory

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发表于2024-12-26

Advanced Topics in the Arithmetic of Elliptic Curves epub 下载 mobi 下载 pdf 下载 txt 电子书下载 2024

Advanced Topics in the Arithmetic of Elliptic Curves pdf epub mobi txt 电子书下载 2024

图书描述

This book continues the treatment of the arithmetic theory of elliptic curves begun in the first volume. The book begins with the theory of elliptic and modular functions for the full modular group r(1), including a discussion of Hekcke operators and the L-series associated to cusp forms. This is followed by a detailed study of elliptic curves with complex multiplication, their associated Grössencharacters and L-series, and applications to the construction of abelian extensions of quadratic imaginary fields. Next comes a treatment of elliptic curves over function fields and elliptic surfaces, including specialization theorems for heights and sections. This material serves as a prelude to the theory of minimal models and Néron models of elliptic curves, with a discussion of special fibers, conductors, and Ogg's formula. Next comes a brief description of q-models for elliptic curves over C and R, followed by Tate's theory of q-models for elliptic curves with non-integral j-invariant over p-adic fields. The book concludes with the construction of canonical local height functions on elliptic curves, including explicit formulas for both archimedean and non-archimedean fields.

Advanced Topics in the Arithmetic of Elliptic Curves 下载 mobi epub pdf txt 电子书