Arithmetic Geometry And Number Theory

By: Iku Nakamura (Editor), Lin Weng (Editor)

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Hardcover | 5 June 2006

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Hardcover
412 Pages

Dimensions(cm)
22.86 x 15.88 x 2.54

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Mathematics is very much a part of our culture; and this invaluable collection serves the purpose of developing the branches involved, popularizing the existing theories and guiding our future explorations.More precisely, the goal is to bring the reader to the frontier of current developments in arithmetic geometry and number theory through the works of Deninger-Werner in vector bundles on curves over p-adic fields; of Jiang on local gamma factors in automorphic representations; of Weng on Deligne pairings and Takhtajan-Zograf metrics; of Yoshida on CM-periods; of Yu on transcendence of special values of zetas over finite fields. In addition, the lecture notes presented by Weng at the University of Toronto from October to November 2005 explain basic ideas and the reasons (not just the language and conclusions) behind Langlands' fundamental, yet notably difficult, works on the Eisenstein series and spectral decompositions.And finally, a brand new concept by Weng called the Geometric Arithmetic program that uses algebraic and/or analytic methods, based on geometric considerations, to develop the promising and yet to be cultivated land of global arithmetic that includes non-abelian Class Field Theory, Riemann Hypothesis and non-abelian Zeta and L Functions, etc.

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You Can Find This Book In

Non-Fiction Mathematics Number Theory Algebra Geometry Algebraic Geometry Booktopia Publisher Services World Scientific Publishing

Foreword	p. v
Preface	p. vii
On Local [Gamma]-Factors	p. 1
Deligne Pairings over Moduli Spaces of Punctured Riemann Surfaces	p. 29
Vector Bundles on Curves over C[subscript p]	p. 47
Absolute CM-periods - Complex and p-Adic	p. 65
Special Zeta Values in Positive Characteristic	p. 103
Automorphic Forms, Eisenstein Series and Spectral Decompositions	p. 123
Geometric Arithmetic: A Program	p. 211
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Arithmetic Geometry And Number Theory

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Hardcover

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