Author | Koblitz, Neal. author |
---|---|

Title | p-adic Numbers, p-adic Analysis, and Zeta-Functions [electronic resource] / by Neal Koblitz |

Imprint | New York, NY : Springer US, 1977 |

Connect to | http://dx.doi.org/10.1007/978-1-4684-0047-2 |

Descript | online resource |

SUMMARY

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 possiยญ 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 topologยญ 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 My treatment is based on Mazur's Bourbaki notes (unpublished)

CONTENT

I p-adic numbers -- 1. Basic concepts -- 2. Metrics on the rational numbers -- 3. Review of building up the complex numbers -- 4. The field of p-adie numbers -- 5. Arithmetic in

Mathematics
Algebra
Mathematics
Algebra