Modular Forms: Basics and Beyond

"Modular Forms: Basics and Beyond" is an advanced textbook that focuses on the topic of modular forms. It is aimed at readers who already have a basic understanding in this area and are looking for more in-depth information. Unlike many other publications that concentrate on elementary aspects, this book offers new perspectives and insights. It comprehensively covers the classical modular forms of one variable and systematically introduces readers to the more complex theories. Key topics include the theory of modular forms with half-integral weight, as well as discussions on theta functions and Eisenstein series, both in holomorphic and non-holomorphic forms. The structure of the book allows readers to gradually learn and understand the theories presented, with a focus on the relationship between forms of half-integral and integral weight, as well as the arithmetic of various Dirichlet series.