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Author:   Neal Koblitz
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2nd ed. 1984
Volume:   58
Dimensions:   Width: 15.50cm , Height: 1.10cm , Length: 23.50cm
Weight:   0.930kg
ISBN:  

9780387960173

ISBN 10:   0387960171
Pages:   153
Publication Date:   23 July 1984
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Table of Contents

I p-adic numbers.- 1. Basic concepts.- 2. Metrics on the rational numbers.- Exercises.- 3. Review of building up the complex numbers.- 4. The field of p-adic numbers.- 5. Arithmetic in ?p.- Exercises.- II p-adic interpolation of the Riemann zeta-function.- 1. A formula for ?(2k).- 2. p-adic interpolation of the function f(s) = as.- Exercises.- 3. p-adic distributions.- Exercises.- 4. Bernoulli distributions.- 5. Measures and integration.- Exercises.- 6. The p-adic ?-function as a Mellin-Mazur transform.- 7. A brief survey (no proofs).- Exercises.- III Building up ?.- 1. Finite fields.- Exercises.- 2. Extension of norms.- Exercises.- 3. The algebraic closure of ?p.- 4. ?.- Exercises.- IV p-adic power series.- 1. Elementary functions.- Exercises.- 2. The logarithm, gamma and Artin-Hasse exponential functions.- Exercises.- 3. Newton polygons for polynomials.- 4. Newton polygons for power series.- Exercises.- V Rationality of the zeta-function of a set of equations over a finite field.- 1. Hypersurfaces and their zeta-functions.- Exercises.- 2. Characters and their lifting.- 3. A linear map on the vector space of power series.- 4. p-adic analytic expression for the zeta-function.- Exercises.- 5. The end of the proof.- Answers and Hints for the Exercises. 

Reviews

From the reviews of the second edition: “In the second edition of this text, Koblitz presents a wide-ranging introduction to the theory of p-adic numbers and functions. … there are some really nice exercises that allow the reader to explore the material. … And with the exercises, the book would make a good textbook for a graduate course, provided the students have a decent background in analysis and number theory.” (Donald L. Vestal, The Mathematical Association of America, April, 2011)

From the reviews of the second edition: In the second edition of this text, Koblitz presents a wide-ranging introduction to the theory of p-adic numbers and functions. ... there are some really nice exercises that allow the reader to explore the material. ... And with the exercises, the book would make a good textbook for a graduate course, provided the students have a decent background in analysis and number theory. (Donald L. Vestal, The Mathematical Association of America, April, 2011)

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