Modular Forms: Basics and Beyond / Goro Shimura

By:

Shimura,Goro

9781461421245

Subject(s):

Mathematics, modular forms

DDC classification:

512.7 ShiM

Summary: 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.

List(s) this item appears in: New Arrivals 01st-15th April 2026, Vol. 07, Issue 06

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Barcode
Books	Indian Institute of Technology Tirupati General Stacks	Mathematics	512.7 ShiM (12527) (Browse shelf(Opens below))	1	Available	12527

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Previous	512.7 NIV/A An Introduction to the Theory of Numbers	512.7 NIV/A An Introduction to the Theory of Numbers	512.7 SerL (12532) Local Fields Graduate Texts in Mathematics	512.7 ShiM (12527) Modular Forms: Basics and Beyond /	512.7 SteA5 (12528) Algebraic Number Theory And Fermats Last Theorem /	512.7 WalD (12531) Diophantine Approximation on Linear Algebraic Groups [Vol. 326]	512.72 CAS/I An introduction to the geometry of numbers	Next

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.

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