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Level: MSci, MSc
Title: Modular forms and arithmetic
Supervisor:

Dr Cecilia Busuioc
Research Area: Algebra
Description:

Modular Forms play a very important role in Arithmetic Number Theory and their study had a tremendous impact in proving famous conjectures like "Fermat's Last Theorem". This project aims to give a basic introduction to the subject following "A Course in Arithmetic" by J.-P. Serre [1]. The main notions at study will be the modular group, lattice functions, the space of modular forms for the full modular group and their Fourier Expansions, Hecke operators and congruence relations.

  1. J.-P. Serre, A Course in Arithmetic. Graduate Texts in Mathematics, Vol. 7, Springer, New York, 1973.
Further Reading:
Key Modules:

MTH5112 Linear Algebra I

MTH6140 Linear Algebra II

MTH5100 Algebraic Structures I

MTH6104 Algebraic Structures II

MTH6128 Number Theory

MTH5103 Complex Variables
Other Information:
Current Availability: Yes