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Modular Forms and L-functions

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Author(s): A. J. Scholl, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part III Lecture Notes
Publisher: University of Cambridge
Year: 2017

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied

Introduction
Some preliminary analysis
Characters of abelian groups
Fourier transforms
Mellin transform and Gamma-function
Riemann zeta-function
Dirichlet L-functions
The modular group
Modular forms of level 1
Basic definitions
The space of modular forms
Arithmetic of Delta
Hecke operators
Hecke operators and algebras
Hecke operators on modular forms
L-functions of eigenforms
Modular forms for subgroups of SL2(Z)
Definitions
The Petersson inner product
Examples of modular forms
Hecke theory for Gamma0(N)
Modular forms and rep theory
Index