Modular Forms: Basics and Beyond (Springer Monographs in Mathematics) 2012th Edition by Shimura (PDF)

Description

This is an advanced book on modular forms. While there are many books published about modular forms, they are written at an elementary level, and not so interesting from the viewpoint of a reader who already knows the basics. This book offers something new, which may satisfy the desire of such a reader. However, we state every definition and every essential fact concerning classical modular forms of one variable. One of the principal new features of this book is the theory of modular forms of half-integral weight, another being the discussion of theta functions and Eisenstein series of holomorphic and nonholomorphic types. Thus the book is presented so that the reader can learn such theories systematically.

User’s Reviews

Editorial Reviews: Review From the reviews:“The book under review is a welcome addition to the existing literature on modular forms. Being written by one of the main contributors to this subject it is designed with great care and love to detailed proofs. … The book is complete in the sense that all statements are clearly formulated and proven in a very rigorous way. … use this book as a guided tour through much of Shimura’s work. Without any doubt this journey is rewarding.” (Stefan Kühnlein, Zentralblatt MATH, Vol. 1234, 2012) From the Back Cover This is an advanced book on modular forms. While there are many books published about modular forms, they are written at an elementary level, and not so interesting from the viewpoint of a reader who already knows the basics. This book offers something new, which may satisfy the desire of such a reader. However, we state every definition and every essential fact concerning classical modular forms of one variable.One of the principal new features of this book is the theory of modular forms of half-integral weight, another being the discussion of theta functions and Eisenstein series of holomorphic and nonholomorphic types. Thus the book is presented so that the reader can learn such theories systematically. Ultimately, we concentrate on the following two themes:(I) The correspondence between the forms of half-integral weight and those of integral weight.(II) The arithmeticity of various Dirichlet series associated with modular forms of integral or half-integral weight.Goro Shimura is currently a professor emeritus of mathematics at Princeton University. About the Author Goro Shimura is currently a professor emeritus of mathematics at Princeton University. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐When I accessed this web page, no reviews appeared for Professor Shimura’s book, and that’s not right. He is a person of great insight. What he writes is not just correct, but done in the most elegant and insightful way. He often writes with great economy. So, whatever he writes is valuable not just for its content but for the precise and insightful organization of the material. Perhaps some pulp novel about vampires will sell more copies, but it would be very difficult to find a book more helpful in honing true understanding and insight. Professor Shimura is an author of world-historical quality, and everyone is well served who reads his book.

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Modular Forms: Basics and Beyond (Springer Monographs in Mathematics) 2012th Edition 2012 PDF Free Download
Download Modular Forms: Basics and Beyond (Springer Monographs in Mathematics) 2012th Edition PDF
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