IMSC Lecture Notes Series

Problems in the Theory of Modular Forms
M. Ram Murty, Michael Dewar and Hester Graves

IMSC b2This book introduces the reader to the fascinating world of modular forms through a problem-solving approach. As such, it can be used by the undergraduate and graduate student for self-instruction. The topics covered include q-series, the modular group, the upper half-plane, modular forms of level one and higher level, the Ramanujan τ -function, the Petersson inner product, Hecke operators, Dirichlet series attached to modular forms and further special topics. It can be viewed as a gentle introduction for a deeper study of the subject. Thus, it is ideal for non-experts seeking an entry into the field.




Contents

Part I Problems
1 Jacobi's q-series
2 The Modular Group
3 The Upper Half-Plane
4 Modular Forms of Level One
5 The Ramanujan τ-function
6 Modular Forms of Higher Level
7 The Petersson Inner Product
8 Hecke Operators of Higher Level
9 Dirichlet Series and Modular Forms
10 Special Topics

Part II Solutions
1 Jacobi's q-series
2 The Modular Group
3 The Upper Half-Plane
4 Modular Forms of Level One
5 The Ramanujan τ-function
6 Modular Forms of Higher Level
7 The Petersson Inner Product
8 Hecke Operators of Higher Level
9 Dirichlet Series and Modular Forms
10 Special Topics
A short guide for further reading
References
Index

IMSC Lecture Notes Series-1
2015, 978-93-80250-72-4, 310 pages, Soft cover, Rs.475.00