# Part III - Modular Forms and L-functions

## Lectured by A. J. Scholl, Lent 2017

These notes are not endorsed by the lecturers, and I have modified them (often significantly) after lectures. They are nowhere near accurate representations of what was actually lectured, and in particular, all errors are almost surely mine.

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# Contents

- V Full version
- 0 Introduction
- 1 Fourier transform
- 2 Mellin transform and Γ-function
- 3 Riemann ζ-function
- 4 Dirichlet L-functions
- 5 The modular group
- 6 Modular forms of level 1
- 7 Hecke operators
- 8 L-functions of eigenforms
- 9 Modular forms for subgroups of SL
_{2}(ℤ) - 10 Hecke theory for Γ
_{0}(N) - 11 Modular forms and rep theory