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arithmetic geometry & number theory lin weng, nakamura [pdf]

Arithmetic Geometry and Number Theory by Lin Weng and Iku Nakamura

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About this book :-
Arithmetic Geometry and Number Theory written by Lin Weng, Iku Nakamura
"Number Theory" is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included.
The collection of this text may be roughly divided into three categories. More precisely, first, Jiang's paper deals with local gamma factors that appeared in the theory of automorphic representations; Obitsu-To-Weng's paper investigates the intrinsic relations between Weil-Petersson and Takhtajan-Zograf metrics on moduli spaces of punctured Riemann surfaces using Deligne pairings and an arithmetic Riemann-Roch isometry; Werner's paper explains her recent works with Deninger on vector bundles on curves over Cp; Yoshida's paper exposes his beautiful theory on CM periods; and Yu's paper studies the transcendence of special values for zetas over finite fields. All these well-prepared articles then bring us to the uppermost frontiers of the current researches in Arithmetic Geometry and Number Theory. Secondly, the lecture notes of Weng explains basic ideas and methods behind the fundamental yet famously difficult work of Langlands on the Eisenstein series and spectral decompositions. The reader will find these notes invaluable in understanding the original theory. Finally, Weng's paper of Geometric Arithmetic outlines a Program for understanding global arithmetic using algebraic and/or analytic methods based on geometric considerations - the topics touched here are a continuation of Weil's approach on non-abelian Class Field Theory using stability and Tannakian category theory; new yet genuine non-abelian zetas and Ls which are closely related with the so-called Arthur's periods; and an intersection approach to the Riemann Hypothesis.

Book Detail :-
Title: Arithmetic Geometry and Number Theory
Edition:
Author(s): Lin Weng, Iku Nakamura
Publisher: World Scientific
Series: Series on number theory and its applications 1
Year: 2006
Pages: 411
Type: PDF
Language: English
ISBN: 9789812568144,981256814X
Country: Japan
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About Author :-
Author Lin Weng , Department of Mathematics, National University Corporation Kyushu University, Japan.
He was Ph.D, from University of Science and Technology, China in 1988. His area of research work was Algebraic, Arithmetic, Complex Geometry and Number Theory
Author Iku Nakamura is professor at Hokkaido University, Japan

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Book Contents :-
Arithmetic Geometry and Number Theory written by Lin Weng, Iku Nakamura cover the following topics.
1. Introduction
2. Basic Properties of Local 7-Factors
3. Local Converse Theorems
4. Poles of Local 7-Factors


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