Modular Forms with Integral and Half-Integral Weights

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9783642293016: Modular Forms with Integral and Half-Integral Weights

"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.

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“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)

“The reader will find a thorough introduction to many central themes in the theory of modular forms of integral and half-integral weight in one variable. ... This monograph is a very valuable addition to the literature on modular forms which will be useful for scholars and for graduate students in this very active branch of number theory.” (Günter Köhler, Zentralblatt MATH, Vol. 1263, 2013)

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