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

(Autor)

Buch | Hardcover
153 Seiten
1984 | 2nd ed. 1984
Springer-Verlag New York Inc.
978-0-387-96017-3 (ISBN)

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p-adic Numbers, p-adic Analysis, and Zeta-Functions - Neal Koblitz
80,24 inkl. MwSt
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).

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. 

Reihe/Serie Graduate Texts in Mathematics ; 58
Zusatzinfo XII, 153 p.
Verlagsort New York, NY
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Arithmetik / Zahlentheorie
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
ISBN-10 0-387-96017-1 / 0387960171
ISBN-13 978-0-387-96017-3 / 9780387960173
Zustand Neuware
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