Modular forms : fundamental tools of mathematics / Claudia Alfes-Neumann.
2021
QA243
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Title
Modular forms : fundamental tools of mathematics / Claudia Alfes-Neumann.
Author
Alfes-Neumann, Claudia.
Uniform Title
Modulformen. English
ISBN
9783658345297 (electronic bk.)
3658345292 (electronic bk.)
9783658345280 (print)
3658345292 (electronic bk.)
9783658345280 (print)
Publication Details
Wiesbaden : Springer, 2021.
Language
English
Description
1 online resource (44 pages)
Item Number
10.1007/978-3-658-34529-7 doi
Call Number
QA243
Dewey Decimal Classification
512.7/3
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 by Springer 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.
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Includes bibliographical references.
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text file
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Source of Description
Online resource; title from PDF title page (SpringerLink, viewed October 25, 2021).
Series
Essentials (Springer VS)
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Modular Forms.
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Table of 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.
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.