Junior Number Theory Seminar
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Mon, 10/05/2010 16:00 |
Damiano Testa (University of Oxford) |
Junior Number Theory Seminar  |
SR1 |
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Mon, 17/05/2010 16:00 |
Frank Gounelas (University of Oxford) |
Junior Number Theory Seminar |
SR1 |
| This talk is the second in a series of an elementary introduction to the ideas unifying elliptic curves, modular forms and Galois representations. I will discuss what it means for an elliptic curve to be modular and what type of representations one associates to such objects. | |||
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Mon, 24/05/2010 16:00 |
Tobias Barthel (University of Oxford) |
Junior Number Theory Seminar |
SR1 |
| In the first half of the talk we explain - in very broad terms - how the objects defined in the previous meetings are linked with each other. We will motivate this 'big picture' by briefly discussing class field theory and the Artin conjecture for L-functions. In the second part we focus on a particular aspect of the theory, namely the L-function preserving construction of elliptic curves from weight 2 newforms via Eichler-Shimura theory. Assuming the Modularity theorem we obtain a proof of the Hasse-Weil conjecture. | |||
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Mon, 31/05/2010 16:00 |
James Maynard (University of Oxford) |
Junior Number Theory Seminar |
SR1 |
| We have seen that L-functions of elliptic curves of conductor N coincide exactly with L-functions of weight 2 newforms of level N from the Modularity Theorem. We will show how, using modular symbols, we can explicitly compute bases of newforms of a given level, and thus investigate L-functions of an elliptic curve of given conductor. In particular, such calculations allow us to numerically test the Birch-Swinnerton-Dyer conjecture. | |||
