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automorphic
Definition
The theory of automorphic function is an intersection of many subjects, which manifests the unity of mathematics.
自守函数理论是多个数学分支交叉的产物，体现了数学的统一性。
He developed a theory of automorphic functions, connecting algebraic and geometric results in his important 1884 book on the icosahedron.
他制定了一个理论，自守函数，连接代数和几何的结果在他的书中重要的1884年的二十面体。
He worked both on ordinary differential equations and on partial differential equations studying abelian integrals, automorphic functions, and functional equations.
他的工作都常微分方程和偏微分方程研究阿贝尔积分， 自守函数，方程和功能。
extraordinary vision that has brought the theory of group representations into a revolutionary new relationship with the theory of automorphic forms and number theory.
非凡的远见，使理论组交涉到一个革命性的新关系理论的自守形式和数量的理论。
a collection of far-reaching and uncannily accurate conjectures relating number theory, automorphic forms, and representation theory.
收集深远和惊讶，准确推测一些有关理论，自守形式， 和 代表性的理论。
Chapter 2 is preliminaries, mainly including some definitions and basic properties on strongly continuous semigroups, integrated semigroups and pseudo al-most automorphic functions.
主要包括强连续半群、积分半群与拟概自守函数的定义与基本性质。
It is of the nature of an induced representation construction-what in the more traditional theory of automorphic forms had been called a 'lifting', known in special cases, and so is covariant (whereas a restricted representation is contravariant).
函子性構想本質上是一種誘導表示構造（在传统的自守形式理论中称为提升，在某些特殊情况下已知），因而是協變的（相反地，受限表示構造是逆變的）。
The quotient of a semisimple Lie group by a compact subgroup is a symmetric space and so the theory of automorphic forms is intimately related to harmonic analysis on symmetric spaces.
半单李群对紧子群的商是对称空间，因此自守形式的理论与对称空间上的调和分析有密切联系。
[Langlands'] astounding insight has provided a whole generation of mathematicians working in automorphic forms and representation theory with a seemingly unlimited expanse of deep, interesting, and above all approachable problems to work away on.
［ 朗兰兹 ｀ ］ 惊人的洞察力提供了整整一代数学家工作的自守形式和代表性理论与看似无限广阔的深入，有趣，尤其是平易近人的问题以外的工作。
In particular he studied automorphic functions in several complex variables, Siegel's modular functions, which have led to a much deeper understanding.
他特别研究自守函数在一些复杂的变数，西格尔的模块化功能，这导致了更深刻的理解。
However Poincaré began publishing an outline of his theory of automorphic functions in 1881 and, as explained in, this led to a competition between the two
但是庞加莱开始出版概述了他的理论，自守函数于1881年，作为解释，这导致了竞争双方：
He investigated the automorphic groups of algebraic Riemann surfaces of genus greater than 1, showing that they were finite.
他调查了自守群体的代数黎曼曲面属大于1 ，表明他们是有限的。
As soon as he had completed his doctoral work, Langlands began to work on automorphic forms.
当他完成了他的博士后工作，朗兰兹开始工作自守形式。
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