Name: p-adic Numbers, p-adic Analysis, and Zeta-Functions By Neal Koblitz
SKU: 9781461270140
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p-adic Numbers, p-adic Analysis, and Zeta-Functions Summary

p-adic Numbers, p-adic Analysis, and Zeta-Functions by Neal Koblitz

The first edition of this work has become the standard introduction to the theory of p-adic numbers at both the advanced undergraduate and beginning graduate level. This second edition includes a deeper treatment of p-adic functions in Ch. 4 to include the Iwasawa logarithm and the p-adic gamma-function, the rearrangement and addition of some exercises, the inclusion of an extensive appendix of answers and hints to the exercises, as well as numerous clarifications.

p-adic Numbers, p-adic Analysis, and Zeta-Functions 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)

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.

Additional information

Sku

NLS9781461270140

ISBN 13

9781461270140

ISBN 10

1461270146

Title

p-adic Numbers, p-adic Analysis, and Zeta-Functions by Neal Koblitz

Author

Neal Koblitz

Series

Graduate Texts in Mathematics

Condition

New

Binding type

Paperback

Publisher

Springer-Verlag New York Inc.

Year published

2012-10-04

Number of pages

153

Prizes

N/A

Cover note

Book picture is for illustrative purposes only, actual binding, cover or edition may vary.

Note

This is a new book - be the first to read this copy. With untouched pages and a perfect binding, your brand new copy is ready to be opened for the first time

p-adic Numbers, p-adic Analysis, and Zeta-Functions Neal Koblitz

p-adic Numbers, p-adic Analysis, and Zeta-Functions by Neal Koblitz

Summary

p-adic Numbers, p-adic Analysis, and Zeta-Functions Summary

p-adic Numbers, p-adic Analysis, and Zeta-Functions by Neal Koblitz

p-adic Numbers, p-adic Analysis, and Zeta-Functions Reviews

Table of Contents

Additional information

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