Lectures on p-adic Differential Equations (Grundlehren der mathematischen Wissenschaften) pdf epub fb2

Lectures on p-adic Differential Equations (Grundlehren der mathematischen Wissenschaften) by - pdf epub fb2

Lectures on p-adic Differential Equations (Grundlehren der mathematischen Wissenschaften) Author: -
Title: Lectures on p-adic Differential Equations (Grundlehren der mathematischen Wissenschaften)
ISBN: 0387907149
ISBN13: 978-0387907147
Other Formats: txt lrf mbr docx
Pages: 310 pages
Publisher: Springer; 1982 edition (November 8, 1982)
Language: English
Category: Science & Math
Size PDF version: 1885 kb
Size EPUB version: 1602 kb
Subcategory: Mathematics




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 ..... .