Modular forms: basics and beyond
(eBook)
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 thebasics. 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.
Shimura, G. (2012). Modular forms: basics and beyond. New York, NY, Springer.
Chicago / Turabian - Author Date Citation (style guide)Shimura, Gorō, 1930-2019. 2012. Modular Forms: Basics and Beyond. New York, NY, Springer.
Chicago / Turabian - Humanities Citation (style guide)Shimura, Gorō, 1930-2019, Modular Forms: Basics and Beyond. New York, NY, Springer, 2012.
MLA Citation (style guide)Shimura, Gorō. Modular Forms: Basics and Beyond. New York, NY, Springer, 2012.
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Last Sierra Extract Time | May 01, 2024 10:09:12 AM |
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Last File Modification Time | May 01, 2024 10:12:59 AM |
Last Grouped Work Modification Time | May 01, 2024 10:09:19 AM |
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245 | 1 | 0 | |a Modular forms :|b basics and beyond /|c Goro Shimura. |
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505 | 0 | |a Preliminaries -- Theta functions and factors -- The rationality and Eisenstein series -- The correspondence between forms of integral and half-integral weight -- The arithmeticity of critical values of Dirichlet series. | |
520 | |a 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 thebasics. 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. | ||
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