The Riemann-Hurwitz Formula

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黎曼的学术遗产：150年巡礼 (英文版) 作者：丘成桐　　 ISBN：978-7-04-031875-3　出版时间：2015-12-16

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Front Matter

What One Should Know About Riemann But May Not Know?

Riemann’s Influence in Geometry, Analysis and Number Theory

Riemann’s Saddle-point Method and the Riemann-Siegel Formula.

The Period Matrices and Theta Functions of Riemann

Riemann’s Hypothesis

Extension of Holomorphic Functions Defined on Non Reduced Analytic Subvarieties

Bundles with Extra Geometric or Dynamic Structure

The Theory of Shock Waves: From Riemann through Today

Riemann’s Existence Theorem

The Historical Roots of the Concept of Riemann Surfaces

The Story of Riemann’s Moduli Space

Riemann and the Modern Concept of Space .

Survey on Analytic and Topological Torsion .

The Riemann Minimal Examples

Manifolds of Mappings and Shapes

The Riemann Hypothesis over Finite Fields: From Weil to the Present Day .

The Riemann-Hurwitz Formula

Early History of the Riemann Hypothesis in Positive Characteristic

Riemann’s Influence in Number Theory from a Computational and Experimental Perspective

Riemann Problem and Shock Capturing Schemes .

A Discourse on the Measurable Riemann Mapping Theorem &Incompressible Fluid Motion

The Mertens Conjecture

Hodge Structures, Coniveau and Algebraic Cycles
- Frans Oort

The Riemann-Hurwitz Formula

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