p-adic Numbers, p-adic Analysis, and Zeta-Functions (1977) (Graduate Texts in Mathematics #58)
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- Synopsis
- 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 possiĀ 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 topologĀ 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 My treatment is based on Mazur's Bourbaki notes (unpublished).
- Copyright:
- 1977
Book Details
- Book Quality:
- Publisher Quality
- ISBN-13:
- 9781468400472
- Related ISBNs:
- 9780387902746
- Publisher:
- Springer New York
- Date of Addition:
- 01/19/21
- Copyrighted By:
- N/A
- Adult content:
- No
- Language:
- English
- Has Image Descriptions:
- No
- Categories:
- Nonfiction, Mathematics and Statistics
- Submitted By:
- Bookshare Staff
- Usage Restrictions:
- This is a copyrighted book.