Web of modularity : arithmetic of the coefficients of modular forms ond Q series

Includes index

Includes bibliography (p. 207-214) and references

1 Basic facts
2 Integer weight modular forms
3 Half-integral weight modular forms
4 Product expansions of modular forms on $\mathrm{SL}_2(\mathbb{Z})$
5 Partitions
6 Weierstrass points on modular curves
7 Traces of singular moduli and class equations
8 Class numbers of quadratic fields
9 Central values of modular $L$-functions and applications
10 Basic hypergeometric generating functions for $L$-values
11 Gaussian hypergeometric functions

Modular forms appear in many ways in number theory. They play a central role in the theory of quadratic forms; in particular, they are generating functions for the number of representations of integers by positive definite quadratic forms. They are also key players in the recent spectacular proof of Fermat's Last Theorem. Modular forms are currently at the center of an immense amount of research activity.