p-adic Numbers, p-adic Analysis, and Zeta-Functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer US
1977
|
| Series: | Graduate Texts in Mathematics
58 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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 My treatment is based on Mazur's Bourbaki notes (unpublished) |
| Physical Description: | 1 Online-Ressource |
| ISBN: | 9781468400472 9781468400496 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4684-0047-2 |
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| spelling | Koblitz, Neal Verfasser aut p-adic Numbers, p-adic Analysis, and Zeta-Functions by Neal Koblitz New York, NY Springer US 1977 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 58 0072-5285 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) Mathematics Mathematics, general Mathematik p-adische Analysis (DE-588)4252360-6 gnd rswk-swf p-adische Zahl (DE-588)4044292-5 gnd rswk-swf Zetafunktion (DE-588)4190764-4 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content p-adische Zahl (DE-588)4044292-5 s Zetafunktion (DE-588)4190764-4 s 2\p DE-604 p-adische Analysis (DE-588)4252360-6 s 3\p DE-604 https://doi.org/10.1007/978-1-4684-0047-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Koblitz, Neal p-adic Numbers, p-adic Analysis, and Zeta-Functions Mathematics Mathematics, general Mathematik p-adische Analysis (DE-588)4252360-6 gnd p-adische Zahl (DE-588)4044292-5 gnd Zetafunktion (DE-588)4190764-4 gnd |
| subject_GND | (DE-588)4252360-6 (DE-588)4044292-5 (DE-588)4190764-4 (DE-588)4123623-3 |
| title | p-adic Numbers, p-adic Analysis, and Zeta-Functions |
| title_auth | p-adic Numbers, p-adic Analysis, and Zeta-Functions |
| title_exact_search | p-adic Numbers, p-adic Analysis, and Zeta-Functions |
| title_full | p-adic Numbers, p-adic Analysis, and Zeta-Functions by Neal Koblitz |
| title_fullStr | p-adic Numbers, p-adic Analysis, and Zeta-Functions by Neal Koblitz |
| title_full_unstemmed | p-adic Numbers, p-adic Analysis, and Zeta-Functions by Neal Koblitz |
| title_short | p-adic Numbers, p-adic Analysis, and Zeta-Functions |
| title_sort | p adic numbers p adic analysis and zeta functions |
| topic | Mathematics Mathematics, general Mathematik p-adische Analysis (DE-588)4252360-6 gnd p-adische Zahl (DE-588)4044292-5 gnd Zetafunktion (DE-588)4190764-4 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik p-adische Analysis p-adische Zahl Zetafunktion Lehrbuch |
| url | https://doi.org/10.1007/978-1-4684-0047-2 |
| work_keys_str_mv | AT koblitzneal padicnumberspadicanalysisandzetafunctions |