Polylogarithmes et mesure de Mahler
The main purpose of this thesis is to compute the logarithmic Mahler measure of the three variable polynomial family xn + 1 + (xn−1 + 1)y + (x − 1)z. In order to accomplish this, we integrate regulators defined on polylogarithmic motivic complexes. To understand these regulators, we explore the properties of polylogarithms and show some polylogarithmic identities. The regulators are then applied to simplify the integrand. Our result is a formula relating the Mahler measure of the family of polynomials to the Bloch–Wigner Dilogarithm and the Riemann zeta function.
Mahler measure Polylogarithm Dilogarithm Regulator Polylogarithmic motivic complex