"Talk on introduction to Mahler measure"의 두 판 사이의 차이
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For a (Laurent) polynomial with complex coefficients, we can define a quantity called the Mahler measure. | 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. | 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 | + | 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. |
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==topics== | ==topics== | ||
2015년 1월 17일 (토) 21:46 판
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