Lectures on p-adic Differential Equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1982
|
| Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
253 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The present work treats p-adic properties of solutions of the hypergeometric differential equation d2 d ~ ( x(l - x) dx + (c(l - x) + (c - 1 - a - b)x) dx - ab)y = 0, 2 with a, b, c in 4) n Zp, by constructing the associated Frobenius structure. For this construction we draw upon the methods of Alan Adolphson [1] in his 1976 work on Hecke polynomials. We are also indebted to him for the account (appearing as an appendix) of the relation between this differential equation and certain L-functions. We are indebted to G. Washnitzer for the method used in the construction of our dual theory (Chapter 2). These notes represent an expanded form of lectures given at the U. L. P. in Strasbourg during the fall term of 1980. We take this opportunity to thank Professor R. Girard and IRMA for their hospitality. Our subject-p-adic analysis-was founded by Marc Krasner. We take pleasure in dedicating this work to him. Contents 1 Introduction . . . . . . . . . . 1. The Space L (Algebraic Theory) 8 2. Dual Theory (Algebraic) 14 3. Transcendental Theory . . . . 33 4. Analytic Dual Theory. . . . . 48 5. Basic Properties of", Operator. 73 6. Calculation Modulo p of the Matrix of ~ f,h 92 7. Hasse Invariants . . . . . . 108 8. The a --+ a' Map . . . . . . . . . . . . 110 9. Normalized Solution Matrix. . . . . .. 113 10. Nilpotent Second-Order Linear Differential Equations with Fuchsian Singularities. . . . . . . . . . . . . 137 11. Second-Order Linear Differential Equations Modulo Powers ofp ..... |
| Physical Description: | 1 Online-Ressource (310p) |
| ISBN: | 9781461381938 9781461381952 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-1-4613-8193-8 |
Staff View
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461381938 9781461381952 |
| issn | 0072-7830 |
| language | English |
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| spelling | Dwork, Bernard Verfasser aut Lectures on p-adic Differential Equations by Bernard Dwork New York, NY Springer New York 1982 1 Online-Ressource (310p) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 253 0072-7830 The present work treats p-adic properties of solutions of the hypergeometric differential equation d2 d ~ ( x(l - x) dx + (c(l - x) + (c - 1 - a - b)x) dx - ab)y = 0, 2 with a, b, c in 4) n Zp, by constructing the associated Frobenius structure. For this construction we draw upon the methods of Alan Adolphson [1] in his 1976 work on Hecke polynomials. We are also indebted to him for the account (appearing as an appendix) of the relation between this differential equation and certain L-functions. We are indebted to G. Washnitzer for the method used in the construction of our dual theory (Chapter 2). These notes represent an expanded form of lectures given at the U. L. P. in Strasbourg during the fall term of 1980. We take this opportunity to thank Professor R. Girard and IRMA for their hospitality. Our subject-p-adic analysis-was founded by Marc Krasner. We take pleasure in dedicating this work to him. Contents 1 Introduction . . . . . . . . . . 1. The Space L (Algebraic Theory) 8 2. Dual Theory (Algebraic) 14 3. Transcendental Theory . . . . 33 4. Analytic Dual Theory. . . . . 48 5. Basic Properties of", Operator. 73 6. Calculation Modulo p of the Matrix of ~ f,h 92 7. Hasse Invariants . . . . . . 108 8. The a --+ a' Map . . . . . . . . . . . . 110 9. Normalized Solution Matrix. . . . . .. 113 10. Nilpotent Second-Order Linear Differential Equations with Fuchsian Singularities. . . . . . . . . . . . . 137 11. Second-Order Linear Differential Equations Modulo Powers ofp ..... Mathematics Global analysis (Mathematics) Analysis Mathematik Differentialgleichung (DE-588)4012249-9 gnd rswk-swf p-adische Differentialgleichung (DE-588)4398266-9 gnd rswk-swf p-adische Zahl (DE-588)4044292-5 gnd rswk-swf Hypergeometrische Differentialgleichung (DE-588)4261657-8 gnd rswk-swf Hypergeometrische Differentialgleichung (DE-588)4261657-8 s p-adische Zahl (DE-588)4044292-5 s 1\p DE-604 Differentialgleichung (DE-588)4012249-9 s 2\p DE-604 p-adische Differentialgleichung (DE-588)4398266-9 s 3\p DE-604 https://doi.org/10.1007/978-1-4613-8193-8 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 | Dwork, Bernard Lectures on p-adic Differential Equations Mathematics Global analysis (Mathematics) Analysis Mathematik Differentialgleichung (DE-588)4012249-9 gnd p-adische Differentialgleichung (DE-588)4398266-9 gnd p-adische Zahl (DE-588)4044292-5 gnd Hypergeometrische Differentialgleichung (DE-588)4261657-8 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4398266-9 (DE-588)4044292-5 (DE-588)4261657-8 |
| title | Lectures on p-adic Differential Equations |
| title_auth | Lectures on p-adic Differential Equations |
| title_exact_search | Lectures on p-adic Differential Equations |
| title_full | Lectures on p-adic Differential Equations by Bernard Dwork |
| title_fullStr | Lectures on p-adic Differential Equations by Bernard Dwork |
| title_full_unstemmed | Lectures on p-adic Differential Equations by Bernard Dwork |
| title_short | Lectures on p-adic Differential Equations |
| title_sort | lectures on p adic differential equations |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Differentialgleichung (DE-588)4012249-9 gnd p-adische Differentialgleichung (DE-588)4398266-9 gnd p-adische Zahl (DE-588)4044292-5 gnd Hypergeometrische Differentialgleichung (DE-588)4261657-8 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Differentialgleichung p-adische Differentialgleichung p-adische Zahl Hypergeometrische Differentialgleichung |
| url | https://doi.org/10.1007/978-1-4613-8193-8 |
| work_keys_str_mv | AT dworkbernard lecturesonpadicdifferentialequations |