Modular Forms with Integral and Half-Integral Weights - Hardcover

From the book reviews:

“The book contains ten chapters. ... this book is a welcome addition for the graduate student or the senior level undergraduate who is looking for a friendly introduction to the topic of modular forms. The book would be ideal for a one-term graduate course or an upper level undergraduate course.” (M. Ram Murty, Mathematical Reviews, May, 2014)

"Modular Forms with Integral and Half-Integral Weights" focuses on the fundamental theory of modular forms of one variable with integral and half-integral weights. The main theme of the book is the theory of Eisenstein series. It is a fundamental problem to construct a basis of the orthogonal complement of the space of cusp forms; as is well known, this space is spanned by Eisenstein series for any weight greater than or equal to 2. The book proves that the conclusion holds true for weight 3/2 by explicitly constructing a basis of the orthogonal complement of the space of cusp forms. The problem for weight 1/2, which was solved by Serre and Stark, will also be discussed in this book. The book provides readers not only basic knowledge on this topic but also a general survey of modern investigation methods of modular forms with integral and half-integral weights. It will be of significant interest to researchers and practitioners in modular forms of mathematics.

Dr. Xueli Wang is a Professor at South China Normal University, China. Dingyi Pei is a Professor at Guangzhou University, China.