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Number Theory in Function Fields

Author:   Michael Rosen
Publisher:   Springer-Verlag New York Inc.
Edition:   2002 ed.
Volume:   210
ISBN:  

9780387953359


Pages:   358
Publication Date:   08 January 2002
Format:   Hardback
Availability:   Out of print, replaced by POD   Availability explained
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Number Theory in Function Fields


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Full Product Details

Author:   Michael Rosen
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2002 ed.
Volume:   210
Dimensions:   Width: 15.60cm , Height: 2.20cm , Length: 23.40cm
Weight:   1.570kg
ISBN:  

9780387953359


ISBN 10:   0387953353
Pages:   358
Publication Date:   08 January 2002
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD   Availability explained
We will order this item for you from a manufatured on demand supplier.

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Reviews

From the reviews: <p>MATHEMATICAL REVIEWS <p> 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 topicsa ]for both number and function fields demonstrates the strong interaction between the respective arithmetics, and allows for motivation on either side. <p>Bulletin of the AMS <p> a ] 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. <p>David Goss (Ohio State University)


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)


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