Modular Forms and String Theory

An introduction to modular forms with string theory and gauge theory applications for students and researchers in physics and mathematics.

A practical introduction to the mathematical theory of modular forms and its physical applications to string theory, suitable for undergraduate and graduate students, and researchers who wish to navigate the intersection of cutting-edge physics and mathematics. This text offers essential insights, examples, and exercises with detailed solutions.An indispensable resource for readers in physics and mathematics seeking a solid grasp of the mathematical tools shaping modern theoretical physics, this book comprises a practical introduction to the mathematical theory of modular forms and their application to the physics of string theory and supersymmetric Yang-Mills theory. Suitable for adventurous undergraduates, motivated graduate students, and researchers wishing to navigate the intersection of cutting-edge research in physics and mathematics, it guides readers from the theory of elliptic functions to the fascinating mathematical world of modular forms, congruence subgroups, Hecke theory, and more. Having established a solid basis, the book proceeds to numerous applications in physics, with only minimal prior knowledge assumed. Appendices review foundational topics, making the text accessible to a broad audience, along with exercises and detailed solutions that provide opportunities for practice. After working through the book, readers will be equipped to carry out research in the field.