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= Tim Dokchitser (Cambridge University): Complex L-functions and the Birch and Swinnerton-Dyer conjecture = == Structure of the course == - Quick review of Elliptic curves over Q and the Mordell-Weil theorem - Elliptic curves over finite fields, heuristics for their distribution and the naive version of BSD - L-functions of elliptic curves and the BSD-conjecture - Root numbers and how to compute them - Parity predictions, Gldfeld's [spelling error on purpose due to antispam filter] conjecture and ranks of elliptic curves over number fields == Prerequisites == Some familiarity with basic algebraic number theory (number fields, primes), and having seen elliptic curves == Computational projects == There will be many small problems and larger assignments to play with, illustrating all the concepts and conjectures from the course |
Tim Dokchitser (Cambridge University): Complex L-functions and the Birch and Swinnerton-Dyer conjecture
Tim Dokchitser (Cambridge University): Complex L-functions and the Birch and Swinnerton-Dyer conjecture
Structure of the course
- - Quick review of Elliptic curves over Q and the Mordell-Weil theorem - Elliptic curves over finite fields, heuristics for their distribution and the naive version of BSD - L-functions of elliptic curves and the BSD-conjecture - Root numbers and how to compute them - Parity predictions, Gldfeld's [spelling error on purpose due to antispam filter] conjecture and ranks of elliptic curves over number fields
Prerequisites
Some familiarity with basic algebraic number theory (number fields, primes), and having seen elliptic curves
Computational projects
There will be many small problems and larger assignments to play with, illustrating all the concepts and conjectures from the course