Modular Forms : Fundamental Tools of Mathematics / by Claudia Alfes-Neumann.

Format:

Book

Author/Creator:

Alfes-Neumann, Claudia.

Series:

Springer essentials, 2731-3115

Language:

English

Subjects (All):

Number theory.

Number Theory.

Local Subjects:

Number Theory.

Physical Description:

1 online resource (44 pages)

Edition:

1st ed. 2021.

Place of Publication:

Wiesbaden : Springer Fachmedien Wiesbaden : Imprint: Springer, 2021.

System Details:

Mode of access: World Wide Web.

Summary:

In this essential, Claudia Alfes-Neumann discusses applications of the theory of modular forms and their importance as fundamental tools in mathematics. These functions - initially defined purely analytically - appear in many areas of mathematics: very prominently in number theory, but also in geometry, combinatorics, representation theory, and physics. After explaining necessary basics from complex analysis, the author defines modular forms and shows some applications in number theory. Furthermore, she takes up two important aspects of the theory surrounding modular forms: Hecke operators and L-functions of modular forms. The essentials concludes with an outlook on real-analytic generalizations of modular forms, which play an important role in current research. This Springer essential is a translation of the original German 1st edition essentials, Modulformen by Claudia Alfes-Neumann, published bySpringer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors. Contents Fundamentals of complex analysis Modular forms Construction of modular forms and examples Hecke theory and L-functions of modular forms The partition function and modular forms of half-integer weight Real-analytic modular forms The target groups Students of mathematics Non-specialist mathematicians and scientists The Author Prof. Dr. Claudia Alfes-Neumann is Professor of Mathematics at Bielefeld University.

Contents:

Fundamentals of complex analysis

Modular forms

Construction of modular forms and examples

Hecke theory as well as L-functions of modular forms

The partition function and modular forms of semi-integer weight

Real-analytic modular forms.

Notes:

Includes bibliographical references and index.

Description based on publisher supplied metadata and other sources.

ISBN:

3-658-34529-2

OCLC:

1276853033