Everytopic Seminar

April 11th,  2008,  1.30 pm – 3.00 pm, Goldsmith 226



Title: The Milnor Ring and Special Values of $L$-functions

Speaker: Glenn Stevens, BU



This will be an elementary talk aimed at a general audience.   We begin with an overview of the theory of modular symbols for $GL_2(\Q)$. The beauty of the theory is in the simplicity of the approach it give us into the theory of special values of $L$-functions.   We proceed by giving a sequence of increasingly more interesting - but always concrete and explicit - examples, explaining how the examples  illuminate the arithmetic theory of special values of $L$-functions attached to modular forms. Our final example will be a modular symbol taking values in Milnor's $K$-theoretic Ring associated to a certain ring of trigonometric functions.  This example generalizes nicely to $GL_n(\Q)$. 

As a simple application, we will see how the theory leads to a simple proof of the classical Dedekind Reciprocity formula.