Lecture 1: Overview
نویسندگان
چکیده
Note: The expression for L(s,W ) requires some care, since q v is a complex number acting on a p-adic vector space. What has to be proved is that the characteristic polynomial for the action of Frobv on W i has rational coefficients (and is independent of p), so evaluation using q v makes sense (and the Riemann Hypothesis ensures absolute convergence of the product in a suitable right half-plane depending only in dimX). We conclude from all this that it is a good idea to study L-functions of reasonable p-adic representations. Representation theory can often be used to fill in the bad factors later.
منابع مشابه
Math 145a Lecture Notes
1 September 2, 2014 5 1.1 Broad Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Introduction to Independence . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Example of Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 More Surprising Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Escaping . . . . . . . . . . . ....
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