Modular Forms (MAGIC049)
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Modular forms (and automorphic forms/representations) play an increasingly central role in modern number theory, but also in other branches of mathematics and even in physics. This course gives an introduction to the subject. Here is a sample of topics we plan to cover:
Prerequisites: Good command of complex analysis and algebra. Occasionally, some knowledge of algebraic number theory and Riemann surface theory would be helpful.
Autumn 2016 (Monday, October 3 to Friday, December 9)
Good command of complex analysis and algebra. Occasionally, some knowledge of algebraic number theory and Riemann surface theory would be helpful.
(1) Modular curves, also as Riemann surfaces and as moduli space of elliptic curves (over C)
(2) Modular functions and forms, basic properties, Eisenstein series, eta-function
(3) Theta series, arithmetic applications
(4) Modular forms and Dirichlet series, functional equation
(5) Hecke operators, Petersson scalar product
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The assessment for this course will be via a single take-home paper in January with 2 weeks to complete and submit online. There will be questions worth 100 marks and you will need 50 marks to pass.
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