Gross-Zagier Formula on Shimura Curves - AMS-184 - Image 1

£148.00

Princeton University Press Gross-Zagier Formula on Shimura Curves - AMS-184

Name: Gross-Zagier Formula on Shimura Curves - AMS-184
Brand: Princeton University Press
Price: 148.0 GBP
Availability: InStock

Geometry & Topology

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Description

This comprehensive mathematical text provides a detailed account of the Gross-Zagier formula on Shimura curves over totally real fields, establishing crucial connections between the heights of Heegner points on abelian varieties and derivatives of L-series. Published by Princeton University Press as volume 184 in the Annals of Mathematics Studies, this work presents significant applications to the Birch and Swinnerton-Dyer conjecture and Diophantine equations. The book begins with a conceptual formulation of the Gross-Zagier formula using incoherent quaternion algebras and incoherent automorphic representations with rational coefficients that naturally attach to abelian varieties parametrized by Shimura curves. The text includes a complete proof of the main theorem, making it an essential reference for researchers in arithmetic geometry, number theory, and the theory of modular forms seeking to understand the profound relationships between algebraic geometry and analytic number theory.

Key Features

The Gross-Zagier formula on Shimura curves over totally real fields provides connections between Heegner point heights and L-series derivatives.

Volume 184 in the Annals of Mathematics Studies series from Princeton University Press features a complete proof of the main theorem.

Applications to the Birch and Swinnerton-Dyer conjecture and Diophantine equations advance understanding of fundamental problems in arithmetic geometry.

Incoherent quaternion algebras and automorphic representations with rational coefficients form the conceptual foundation of the mathematical framework presented.

Product Specifications

Brand: Princeton University Press
Format: hardcover
ASIN: 0691155917
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Geometry & Topology
Domain: Amazon UK
Release Date: 04 January 2013
Listed Since: 24 April 2012

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Princeton University Press Gross-Zagier Formula on Shimura Curves - AMS-184

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