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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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