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 considered in attempts to find large primes. And later it appeared as a tool in transcendental number theory. In more recent times it has become an active area of research due to its appearances in many places. There are many conjectural formula relating Mahler measures to special values of L-functions of elliptic curves and they also appear in hyperbolic geometry. 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

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