Lectures on p-adic Differential Equations

Released on by Bernard Dwork
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  • Lectures on p-adic Differential Equations Book Detail

  • Author : Bernard Dwork
  • Release Date : 2012-12-06
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 318
  • ISBN 13 : 1461381932
  • File Size : 99,99 MB
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Lectures on p-adic Differential Equations by Bernard Dwork PDF Summary

Book 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 ..... .

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Lectures on p-adic Differential Equations

Lectures on p-adic Differential Equations

File Size : 88,88 MB
Total View : 5392 Views
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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)

Lectures on P-adic Differential Equations

Lectures on P-adic Differential Equations

File Size : 80,80 MB
Total View : 7745 Views
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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

p-adic Differential Equations

p-adic Differential Equations

File Size : 6,6 MB
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A detailed and unified treatment of $P$-adic differential equations, from the basic principles to the current frontiers of research.

p-adic Differential Equations

p-adic Differential Equations

File Size : 99,99 MB
Total View : 3780 Views
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Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to