Linear Mahler measures and double L-values of modular forms

Speaker: Dr. Masha Vlasenko (TCD)

Time: 4:00PM

Date: Thu 5th April 2012

Location: Mathematical Sciences Seminar Room (Ag 1.01)

There are plenty of examples and conjectures where the Mahler measure of a Laurent polynomial in several variables is equal to a special value of a certain L-function. The simplest linear Mahler measures M_n=m(1+x_1+...+x_n) were computed by Smyth for n=2, 3 about 30 years ago and are not yet evaluated for larger n. Rodriguez-Villegas showed that both of these cases can be treated using modular forms. We develop his approach and represent M_3 and M_4 as double L-values of pairs of certain modular forms. Unfortunately the forms appear to be meromorphic in the most interesting case n=4. This is joint work with Evgeny Shinder.

(This talk is part of the K-Theory, Quadratic Forms and Number Theory series.)