Talk on introduction to Mahler measure

abstract

For a (Laurent) polynomial with complex coefficients, we can define a quantity called the Mahler measure. They appeared in study to find large primes and later as a tool in transcendental number theory. More suprisingly, there are many known conjectural relationship between Mahler measure of multivariate polynomials and special values of L-functions of elliptic curves. They also appear in the study of hyperbolic 3-manifolds. In this talk, I will give an introductory survey on the topic.

topics

• finding large primes
• Lehmer's conjecture
• Smyth's formula
• Mahler's multivariate generalization
• elliptic L-values
• hyperbolic geometry