Problems in the Theory of Modular Forms

This 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 ? -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.