Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Graduate Texts in Mathematics (GTM, volume 210)
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Table of contents (17 chapters)
Reviews
From the reviews:
MATHEMATICAL REVIEWS
"Both in the large (choice and arrangement of the material) and in the details (accuracy and completeness of proofs, quality of explanations and motivating remarks), the author did a marvelous job. His parallel treatment of topics…for both number and function fields demonstrates the strong interaction between the respective arithmetics, and allows for motivation on either side."
Bulletin of the AMS
"… Which brings us to the book by Michael Rosen. In it, one has an excellent (and, to the author's knowledge, unique) introduction to the global theory of function fields covering both the classical theory of Artin, Hasse, Weil and presenting an introduction to Drinfeld modules (in particular, the Carlitz module and its exponential). So the reader will find the basic material on function fields and their history (i.e., Weil differentials, the Riemann-Roch Theorem etc.) leading up to Bombieri's proof of the Riemann hypothesis first established by Weil. In addition one finds chapters on Artin's primitive root Conjecture for function fields, Brumer-Stark theory, the ABC Conjecture, results on class numbers and so on. Each chapter contains a list of illuminating exercises. Rosen's book is perfect for graduate students, as well as other mathematicians, fascinated by the amazing similarities between number fields and function fields."
David Goss (Ohio State University)
Authors and Affiliations
Bibliographic Information
Book Title: Number Theory in Function Fields
Authors: Michael Rosen
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4757-6046-0
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 2002
Hardcover ISBN: 978-0-387-95335-9Published: 08 January 2002
Softcover ISBN: 978-1-4419-2954-9Published: 03 December 2010
eBook ISBN: 978-1-4757-6046-0Published: 18 April 2013
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XI, 358
Topics: Number Theory, Algebraic Geometry, Field Theory and Polynomials