Introduction to Applications of Modular Forms

This book is a self-contained treatment for those who study or work on the computational aspects of classical modular forms. The author describes the theory of modular forms and its applications in number theoretic problems such as representations by quadratic forms and the determination of asymptotic formulas for Fourier coefficients of different types of special functions. A detailed account of recent applications of modular forms in number theory with a focus on using computer algorithms is provided. Computer algorithms are included for each presented application to help readers put the theory in context and make new conjectures. In addition, this book: - Describes the theory of modular forms and its applications in number theoretic problems - Provides a resource for people who study or work on the computational aspects of classical modular forms - Includes computer algorithms to help readers conjecture new results and prove them using the presented theory