P-adic numbers, p-adic analysis, and zeta-functions
著者
書誌事項
P-adic numbers, p-adic analysis, and zeta-functions
（Graduate texts in mathematics, 58）
Springer-Verlag, c1984
2nd ed
- : U.S.
- : Germany
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注記
Bibliography: p. 129-131
Includes index
内容説明・目次
- 巻冊次
-
: U.S. ISBN 9780387960173
内容説明
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.
目次
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.
- 巻冊次
-
: Germany ISBN 9783540960171
内容説明
This volume in the Graduate Texts in Mathematics series, looks at p-adic numbers and considers such topics as the Riemann zeta-function and the rationality of the zeta-function of a set of equations over a finite field.
目次
- P-adic numbers
- p-adic interpolation of the reimann zeta-function
- p-adic power series
- rationality of the zeta-function of a set of equations over a finite field (Part contents).
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