Integrated MSc-PhD Program SYLLABUS |
KSM4E09: Modular Forms |
Topics covered include the modular group and congruence subgroups, the definition of modular forms and their first properties, Eisenstein series, theta series, valence formulas, Hecke operators, Atkin-Lehner-Li theory, L-functions, modular curves, and modularity. The final lectures will provide a global outlook on the use of modular forms (and their associated Galois representations) in solving Diophantine equations, particularly Fermat’s Last Theorem. Suggested texts:
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