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Basic Structures of Function Field Arithmetic

โœ Scribed by Goss D.

Publisher
Springer
Year
1996
Tongue
English
Leaves
439
Series
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in Mathematics
Edition
1
Category
Library
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โœฆ Synopsis

From the reviews:"The book...is a thorough and very readable introduction to the arithmetic of function fields of one variable over a finite field, by an author who has made fundamental contributions to the field. It serves as a definitive reference volume, as well as offering graduate students with a solid understanding of algebraic number theory the opportunity to quickly reach the frontiers of knowledge in an important area of mathematics...The arithmetic of function fields is a universe filled with beautiful surprises, in which familiar objects from classical number theory reappear in new guises, and in which entirely new objects play important roles. Goss'clear exposition and lively style make this book an excellent introduction to this fascinating field." MR 97i:11062

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1. Additive Polynomials -- 2. Review of Non-Archimedean Analysis -- 3. The Carlitz Module -- 4. Drinfeld Modules -- 5. T-modules -- 6. Shtukas -- 7. Sign Normalized Rank 1 Drinfeld Modules -- 8. L-series -- 9. [Gamma]-functions -- 10. Additional Topics

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This book provides an exposition of function field arithmetic with emphasis on recent developments concerning Drinfeld modules, the arithmetic of special values of transcendental functions (such as zeta and gamma functions and their interpolations), diophantine approximation and related interesting

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โœ Dinesh S. Thakur ๐Ÿ“‚ Library ๐Ÿ“… 2004 ๐Ÿ› World Scientific Publishing Co Pte Ltd ๐ŸŒ English

This book provides an exposition of function field arithmetic with emphasis on recent developments concerning Drinfeld modules, the arithmetic of special values of transcendental functions (such as zeta and gamma functions and their interpolations), diophantine approximation and related interesting