Description

Book Synopsis
Develops an arithmetic analog of the theory of ordinary differential equations, where functions are replaced by integer numbers, the derivative operator is replaced by a 'Fermat quotient operator', and differential equations (viewed as functions on jet spaces) are replaced by 'arithmetic differential equations'.

Table of Contents
Main concepts and results: Preliminaries from algebraic geometry Outline of $\delta$-geometry General theory: Global theory Local theory Birational theory Applications: Spherical correspondences Flat correspondences Hyperbolic correspondences List of results Bibliography Index.

Arithmetic Differential Equations

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    A Hardback by Alexandru Buium

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      Book details

      Publisher American Mathematical Society
      Published 9/30/2005 12:00:00 AM
      ISBN-13 9780821838624
      978-0821838624
      ISBN-10 0821838628

      Description

      Book Synopsis
      Develops an arithmetic analog of the theory of ordinary differential equations, where functions are replaced by integer numbers, the derivative operator is replaced by a 'Fermat quotient operator', and differential equations (viewed as functions on jet spaces) are replaced by 'arithmetic differential equations'.

      Table of Contents
      Main concepts and results: Preliminaries from algebraic geometry Outline of $\delta$-geometry General theory: Global theory Local theory Birational theory Applications: Spherical correspondences Flat correspondences Hyperbolic correspondences List of results Bibliography Index.

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