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p-adic Numbers, p-adic Analysis, and Zeta-Functions (2nd edition, Graduate Tex..
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eBay item number:267353123104
Item specifics
- Condition
- Very Good
- Seller Notes
- Country of Origin
- Switzerland
- Book Title
- p-adic Numbers, p-adic Analysis, and Zeta-Functions (2nd edition
- Genre
- Mathematics & Sciences
- Topic
- Mathematics
- ISBN
- 9781461270140
About this product
Product Identifiers
Publisher
Springer New York
ISBN-10
1461270146
ISBN-13
9781461270140
eBay Product ID (ePID)
159795352
Product Key Features
Number of Pages
Xii, 153 Pages
Publication Name
P-Adic Numbers, P-Adic Analysis, and Zeta-Functions
Language
English
Subject
Functional Analysis, Algebra / General, Number Theory, Mathematical Analysis
Publication Year
2012
Type
Textbook
Subject Area
Mathematics
Series
Graduate Texts in Mathematics Ser.
Format
Trade Paperback
Dimensions
Item Height
0.1 in
Item Weight
9.4 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Edition Number
2
Intended Audience
Scholarly & Professional
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)
Series Volume Number
58
Number of Volumes
1 vol.
Illustrated
Yes
Table Of Content
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.
Synopsis
Neal Koblitz was a student of Nicholas M. Katz, under whom he received his Ph.D. in mathematics at Princeton in 1974. He spent the year 1974 -75 and the spring semester 1978 in Moscow, where he did research in p -adic analysis and also translated Yu. I. Manin's "Course in Mathematical Logic" (GTM 53). He taught at Harvard from 1975 to 1979, and since 1979 has been at the University of Washington in Seattle. He has published papers in number theory, algebraic geometry, and p-adic analysis, and he is the author of "p-adic Analysis: A Short Course on Recent Work" (Cambridge University Press and GTM 97: "Introduction to Elliptic Curves and Modular Forms (Springer-Verlag)., The most important revision in the second edition are the enlargment of the 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, and numerous corrections and clarifications. The first edition has become the standard introduction to the theory of p-adic numbers on the advanced undergraduate and beginning graduate level., This work has become the standard introduction to the theory of p-adic numbers. The 2nd edition adds a deeper treatment of p-adic functions, including the Iwasawa logarithm and the p-adic gamma-function, plus new exercises and an appendix of answers and hints.
LC Classification Number
QA150-272
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Seller feedback (2,144)
- d***n (792)- Feedback left by buyer.Past 6 monthsVerified purchaseTypically bungling performance from Evri (Hermes): the package was said to be ‘out for delivery’ on 2 September, but it did not arrive until 8 September, after I had expended much effort in trying to find out what had happened to it. In contrast, top marks for the seller: accurate description, excellent packaging, prompt transport from USA (until Evri got its hands on the package), and good-natured support when I explained the problems I was having with the notoriously inefficient delivery firm.
- t***j (1746)- Feedback left by buyer.Past 6 monthsVerified purchaseGreat Transaction - Item as Described - Packaged with Great Care - Fast Shipping - Many Thanks! A+++The Book Club of California: (Volume 87, No. 1, Winter 2022) (#405979437934)
- k***d (125)- Feedback left by buyer.Past 6 monthsVerified purchaseShipping was insanely fast! Packaging super tough! Came as described and beyond the value. One of my new favorite additions to my books.Mount Analogue: An Authentic Narrative (#405833804341)