P Adic Numbers P Adic Analysis And Zeta Functions
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p-adic Numbers, p-adic Analysis, and Zeta-Functions
Author: NEAL Koblitz
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
These lecture notes are intended as an introduction to p-adic analysis on the elementary level. For this reason they presuppose as little background as possi ble. Besides about three semesters of calculus, I presume some slight exposure to more abstract mathematics, to the extent that the student won't have an adverse reaction to matrices with entries in a field other than the real numbers, field extensions of the rational numbers, or the notion of a continuous map of topolog ical spaces. The purpose of this book is twofold: to develop some basic ideas of p-adic analysis, and to present two striking applications which, it is hoped, can be as effective pedagogically as they were historically in stimulating interest in the field. The first of these applications is presented in Chapter II, since it only requires the most elementary properties of Q ; this is Mazur's construction by p means of p-adic integration of the Kubota-Leopoldtp-adic zeta-function, which "p-adically interpolates" the values of the Riemann zeta-function at the negative odd integers. My treatment is based on Mazur's Bourbaki notes (unpublished).
A Course in p-adic Analysis
Author: Alain M. Robert
language: en
Publisher: Springer Science & Business Media
Release Date: 2000-05-31
Discovered at the turn of the 20th century, p-adic numbers are frequently used by mathematicians and physicists. This text is a self-contained presentation of basic p-adic analysis with a focus on analytic topics. It offers many features rarely treated in introductory p-adic texts such as topological models of p-adic spaces inside Euclidian space, a special case of Hazewinkel’s functional equation lemma, and a treatment of analytic elements.
The Riemann Zeta-Function
Author: Anatoly A. Karatsuba
language: en
Publisher: Walter de Gruyter
Release Date: 2011-05-03
No detailed description available for "The Riemann Zeta-Function".