Koblitz N. p-adic Numbers, p-adic Analysis, and Zeta-Functions

2nd Edition. — Springer-Verlag, 1984. — xii, 153 p. — (Graduate Texts in Mathematics, 58) — ISBN 978-1-4612-7014-0, 978-1-4612-1112-9.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.
The most important revisions in this edition are: (1) enlargement of the treatment of p-adic functions in Chapter IV to inc1ude the Iwasawa logarithm and the p-adic gamma-function, (2) re arrangement and addition of so me exercises, (3) inc1usion of an extensive appendix of answers and hints to the exercises, the absence of which from the first edition was apparently a source of considerable frustration for many readers, and (4) numerous corrections and c1arifications, most of wh ich were proposed by readers who took the trouble to write me. Some c1arifications in Chapters IV and V were also suggested by V. V. Shokurov, the translator of the Russian edition.
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).Файл: отскан. стр. (b/w 600 dpi) + OCR