Talk on introduction to Mahler measure

abstract

For a (Laurent) polynomial with complex coefficients, we can define a quantity called the Mahler measure. It was originally studied in attempts to find large primes. And later its multivariate version was introduced as a tool in transcendental number theory. In more recent times it has become an active area of research due to its mysterious connections with many other subjects. For example, there are many conjectural formulas relating Mahler measures to special values of L-functions of elliptic curves and they also show up in hyperbolic geometry. In this talk, I will give an introductory survey on this topic.

topics

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

related items

• Mahler measure
• Mahler measure and L-values of elliptic curves
• Mahler measure, hyperbolic geometry and dilogarithm