Armin Straub
Log-sine evaluations of Mahler measures.
Tue, 03/22/2011 - 16:01 — SomNambulAuthors: Jonathan M. Borwein, Armin Straub
Subjects: Classical Analysis and ODEs
AbstractWe provide evaluations of several recently studied higher and multiple Mahler
measures using log-sine integrals. This is complemented with an analysis of
generating functions and identities for log-sine integrals which allows the
evaluations to be expressed in terms of zeta values or more general
polylogarithmic terms. The machinery developed is then applied to evaluation of
further families of multiple Mahler measures.Log-sine evaluations of Mahler measures, II.
Thu, 03/17/2011 - 16:01 — SomNambulAuthors: James Wan, David Borwein, Jonathan M. Borwein, Armin Straub
Subjects: Classical Analysis and ODEs
AbstractWe continue the analysis of higher and multiple Mahler measures using
log-sine integrals as started in "Log-sine evaluations of Mahler measures" and
"Special values of generalized log-sine integrals" by two of the authors. This
motivates a detailed study of various multiple polylogarithms and worked
examples are given. Our techniques enable the reduction of several multiple
Mahler measures, and supply an easy proof of two conjectures by Boyd.
User login
