Arithmetic Study Group: Multiple L-values and periods of integrals
8 March 2005 14:00 in CM219
"There are generalizations of the Riemann zeta function to functions of several variables called the multiple zeta functions. Like the usual zeta function, their values at positive integer points, called multiple zeta values, are interesting. While originally defined by Euler, recently these numbers have been studied from a different point of view. It turns out that there are several relations between them and the algebra of multiple zeta values is very interesting. Further they are periods in the sense of Kontsevich and Zagier and in fact they appear as periods of a mixed Hodge structure on the fundamental group of the complex projective plane with the points 0,1 and the point at infinity removed. In this talk we define a generalization of such numbers called multiple L-values of modular forms. We show that they have similar properties to the multiple zeta values and further, some of the values are periods. In some cases we can show that these numbers are periods of a mixed Hodge structure on the fundamental group of a modular curve."