Arithmetic differential operators over the p-adic integers:
The study of arithmetic differential operators is a novel and promising area of mathematics. This complete introduction to the subject starts with the basics: a discussion of p-adic numbers and some of the classical differential analysis on the field of p-adic numbers leading to the definition of ar...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2012
|
| Series: | London Mathematical Society lecture note series
396 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | The study of arithmetic differential operators is a novel and promising area of mathematics. This complete introduction to the subject starts with the basics: a discussion of p-adic numbers and some of the classical differential analysis on the field of p-adic numbers leading to the definition of arithmetic differential operators on this field. Buium's theory of arithmetic jet spaces is then developed succinctly in order to define arithmetic operators in general. Features of the book include a comparison of the behaviour of these operators over the p-adic integers and their behaviour over the unramified completion, and a discussion of the relationship between characteristic functions of p-adic discs and arithmetic differential operators that disappears as soon as a single root of unity is adjoined to the p-adic integers. This book is essential reading for researchers and graduate students who want a first introduction to arithmetic differential operators over the p-adic integers |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (vi, 139 pages) |
| ISBN: | 9781139084666 |
| DOI: | 10.1017/CBO9781139084666 |
Staff View
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| 520 | |a The study of arithmetic differential operators is a novel and promising area of mathematics. This complete introduction to the subject starts with the basics: a discussion of p-adic numbers and some of the classical differential analysis on the field of p-adic numbers leading to the definition of arithmetic differential operators on this field. Buium's theory of arithmetic jet spaces is then developed succinctly in order to define arithmetic operators in general. Features of the book include a comparison of the behaviour of these operators over the p-adic integers and their behaviour over the unramified completion, and a discussion of the relationship between characteristic functions of p-adic discs and arithmetic differential operators that disappears as soon as a single root of unity is adjoined to the p-adic integers. This book is essential reading for researchers and graduate students who want a first introduction to arithmetic differential operators over the p-adic integers | ||
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Record in the Search Index
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| author | Ralph, Claire C. |
| author_facet | Ralph, Claire C. |
| author_role | aut |
| author_sort | Ralph, Claire C. |
| author_variant | c c r cc ccr |
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| bvnumber | BV043942276 |
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| contents | The p-adic numbers Qp -- Some classical analysis on Qp -- The Artin-Hasse exponential function -- The completion of the algebraic closure of Qp -- Zeta functions -- Analytic functions on Zp -- Arithmetic differential operators on Zp -- A general view of arithmetic differential operators -- Analyticity of arithmetic differential operators -- Characteristic functions of discs in Zp: p-adic coordinates -- Characteristic functions of discs in Zp: harmonic coordinates -- Some differences between (Se(B-operators over Zp and Zur p |
| ctrlnum | (ZDB-20-CBO)CR9781139084666 (OCoLC)859644185 (DE-599)BVBBV043942276 |
| dewey-full | 515.7242 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7242 |
| dewey-search | 515.7242 |
| dewey-sort | 3515.7242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781139084666 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9781139084666 |
| language | English |
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| spelling | Ralph, Claire C. Verfasser aut Arithmetic differential operators over the p-adic integers Claire C. Ralph, Santiago R. Simanca Cambridge Cambridge University Press 2012 1 online resource (vi, 139 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 396 Title from publisher's bibliographic system (viewed on 05 Oct 2015) The p-adic numbers Qp -- Some classical analysis on Qp -- The Artin-Hasse exponential function -- The completion of the algebraic closure of Qp -- Zeta functions -- Analytic functions on Zp -- Arithmetic differential operators on Zp -- A general view of arithmetic differential operators -- Analyticity of arithmetic differential operators -- Characteristic functions of discs in Zp: p-adic coordinates -- Characteristic functions of discs in Zp: harmonic coordinates -- Some differences between (Se(B-operators over Zp and Zur p The study of arithmetic differential operators is a novel and promising area of mathematics. This complete introduction to the subject starts with the basics: a discussion of p-adic numbers and some of the classical differential analysis on the field of p-adic numbers leading to the definition of arithmetic differential operators on this field. Buium's theory of arithmetic jet spaces is then developed succinctly in order to define arithmetic operators in general. Features of the book include a comparison of the behaviour of these operators over the p-adic integers and their behaviour over the unramified completion, and a discussion of the relationship between characteristic functions of p-adic discs and arithmetic differential operators that disappears as soon as a single root of unity is adjoined to the p-adic integers. This book is essential reading for researchers and graduate students who want a first introduction to arithmetic differential operators over the p-adic integers Differential operators Arithmetic functions p-adic numbers Differentialoperator (DE-588)4012251-7 gnd rswk-swf p-adische Zahl (DE-588)4044292-5 gnd rswk-swf Differentialoperator (DE-588)4012251-7 s p-adische Zahl (DE-588)4044292-5 s 1\p DE-604 Simanca, S. R. Sonstige oth Erscheint auch als Druckausgabe 978-1-107-67414-1 https://doi.org/10.1017/CBO9781139084666 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ralph, Claire C. Arithmetic differential operators over the p-adic integers The p-adic numbers Qp -- Some classical analysis on Qp -- The Artin-Hasse exponential function -- The completion of the algebraic closure of Qp -- Zeta functions -- Analytic functions on Zp -- Arithmetic differential operators on Zp -- A general view of arithmetic differential operators -- Analyticity of arithmetic differential operators -- Characteristic functions of discs in Zp: p-adic coordinates -- Characteristic functions of discs in Zp: harmonic coordinates -- Some differences between (Se(B-operators over Zp and Zur p Differential operators Arithmetic functions p-adic numbers Differentialoperator (DE-588)4012251-7 gnd p-adische Zahl (DE-588)4044292-5 gnd |
| subject_GND | (DE-588)4012251-7 (DE-588)4044292-5 |
| title | Arithmetic differential operators over the p-adic integers |
| title_auth | Arithmetic differential operators over the p-adic integers |
| title_exact_search | Arithmetic differential operators over the p-adic integers |
| title_full | Arithmetic differential operators over the p-adic integers Claire C. Ralph, Santiago R. Simanca |
| title_fullStr | Arithmetic differential operators over the p-adic integers Claire C. Ralph, Santiago R. Simanca |
| title_full_unstemmed | Arithmetic differential operators over the p-adic integers Claire C. Ralph, Santiago R. Simanca |
| title_short | Arithmetic differential operators over the p-adic integers |
| title_sort | arithmetic differential operators over the p adic integers |
| topic | Differential operators Arithmetic functions p-adic numbers Differentialoperator (DE-588)4012251-7 gnd p-adische Zahl (DE-588)4044292-5 gnd |
| topic_facet | Differential operators Arithmetic functions p-adic numbers Differentialoperator p-adische Zahl |
| url | https://doi.org/10.1017/CBO9781139084666 |
| work_keys_str_mv | AT ralphclairec arithmeticdifferentialoperatorsoverthepadicintegers AT simancasr arithmeticdifferentialoperatorsoverthepadicintegers |