By Nicholas M. Katz
This e-book is worried with parts of arithmetic, at the beginning sight disjoint, and with a few of the analogies and interactions among them. those parts are the idea of linear differential equations in a single advanced variable with polynomial coefficients, and the idea of 1 parameter households of exponential sums over finite fields. After reviewing a few effects from illustration thought, the publication discusses effects approximately differential equations and their differential galois teams (G_) and one-parameter households of exponential sums and their geometric monodromy teams (G). the ultimate a part of the e-book is dedicated to comparability theorems referring to G and G_ of certainly "corresponding" occasions, which offer a scientific clarification of the impressive "coincidences" discovered "by hand" within the hypergeometric case.
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Extra resources for Exponential Sums and Differential Equations
Example 2-1g: Plot a cross at current position Enter the "Kruis" command K (Kruis means cross in Dutch): K
Plot the Trajectory: T
For example, you can draw a box around the plotted trajectory by locating the "Box" command in the menu system and executing it. To locate the "Box" command, hit
Exponential Sums and Differential Equations by Nicholas M. Katz