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

✍ Scribed by Neal Koblitz

• Publisher: Springer
• Year: 1984
• Tongue: English
• Leaves: 162
• Series: Graduate Texts in Mathematics 58
• Edition: 2
• Category: Library

✦ 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).

✦ Table of Contents

Front Matter....Pages i-xii
p -adic numbers....Pages 1-20
p -adic interpolation of the Riemann zeta-function....Pages 21-51
Building up Ω....Pages 52-75
p -adic power series....Pages 76-108
Rationality of the zeta-function of a set of equations over a finite field....Pages 109-128
Back Matter....Pages 129-153

✦ Subjects

Number Theory; Analysis