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Catalogue Information
Field name	Details
Dewey Class	512
Title	p-adic Numbers, p-adic Analysis, and Zeta-Functions ([EBook]) / by Neal Koblitz.
Author	Koblitz, Neal. , 1948-
Other name(s)	SpringerLink (Online service)
Edition statement	Second Edition.
Publication	New York, NY : Springer , 1984.
Physical Details	XII, 153 pages : online resource.
Series	Graduate texts in mathematics 0072-5285 ; ; 58
ISBN	9781461211129
Summary Note	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).:
Contents note	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. .
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4612-1112-9
Links to Related Works	Subject References: Algebra . Analysis . Analysis (Mathematics) . Mathematical analysis . Mathematics . Number Theory . Authors: Koblitz, Neal. 1948- . Koblitz, Neal, 1948- . Corporate Authors: SpringerLink (Online service) . Series: Graduate texts in mathematics . GTM . Classification: 512 .

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

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