Lectures on p-adic Differential Equations

Produkt bewerten

Bernard Dwork

Verlag:

Springer Verlag

Unsere-Artikel-Nr.: 627RKYW

EAN: 9781461381952

Erhältlich:

Nicht auf Lager

Zustellung: Di, 16.06.2026

Versand: Kostenlos

-6.4 %

CHF 134.–

CHF 125.40

Beschreibung

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..

Spezifikationen

Sprache

Englisch

Autor

Bernard Dwork

Kollektion

Grundlehren der mathematischen Wissenschaften

Erscheinungsjahr

2011

Erscheinungsland

Format

Buch (Softcover)

Anzahl Seiten