Abstract: In 2005 Doug Lind extended the concept of the Mahler measure of a polynomial with integer coefficients to the Lind-Mahler measure of a linear sum of characters for an arbitrary compact abelian group (the classical Mahler measure corresponding to G=R/Z). Each of these groups then has a Lind-Lehmer problem. In 1977 Olga Taussky-Todd asked for a characterization of the values of the group determinant when the entries are integers, with particular interest in the cyclic groups where these are the integer circulant determinants. For finite abelian groups the values of the Lind-Mahler measure correspond exactly to the integer group determinants. In particular this gives us a way to extend the Lind-Mahler measure to finite non-abelian groups. I will talk about the progress that has been made on the Lind-Lehmer Problem and the Taussky-Todd integer group determinant problem. |