東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Modular forms = fundamental tools of...

Alfes-Neumann, Claudia.

Linked to FindBook

Google Book

Amazon

博客來

Modular forms = fundamental tools of mathematics /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Modular forms/ by Claudia Alfes-Neumann.
Reminder of title:	fundamental tools of mathematics /
Author:	Alfes-Neumann, Claudia.
Published:	Wiesbaden :Springer Fachmedien Wiesbaden : : 2021.,
Description:	vii, 41 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Forms, Modular. -
Online resource:	https://doi.org/10.1007/978-3-658-34529-7
ISBN:	9783658345297

Modular forms = fundamental tools of mathematics /
Alfes-Neumann, Claudia.

Modular formsfundamental tools of mathematics /[electronic resource] :by Claudia Alfes-Neumann. - Wiesbaden :Springer Fachmedien Wiesbaden :2021. - vii, 41 p. :ill., digital ;24 cm. - essentials. - essentials..

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.

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.

ISBN: 9783658345297

Standard No.: 10.1007/978-3-658-34529-7doiSubjects--Topical Terms:

540521
Forms, Modular.

LC Class. No.: QA243 / .A54 2021

Dewey Class. No.: 512.73

Modular forms = fundamental tools of mathematics /
LDR:03127nmm a2200349 a 4500 001 2253759
003 DE-He213
005 20211011100526.0
006 m d
007 cr nn 008maaau
008 220327s2021 gw s 0 eng d
020 $a 9783658345297 $q (electronic bk.)
020 $a 9783658345280 $q (paper)
024 7 $a 10.1007/978-3-658-34529-7 $2 doi
035 $a 978-3-658-34529-7
040 $a GP $c GP
041 1 $a eng $h ger
050 4 $a QA243 $b .A54 2021
072 7 $a PBH $2 bicssc
072 7 $a MAT022000 $2 bisacsh
072 7 $a PBH $2 thema
082 0 4 $a 512.73 $2 23
090 $a QA243 $b .A386 2021
100 1 $a Alfes-Neumann, Claudia. $3 3522287
240 1 0 $a Modulformen. $l English
245 1 0 $a Modular forms $h [electronic resource] : $b fundamental tools of mathematics / $c by Claudia Alfes-Neumann.
260 $a Wiesbaden : $b Springer Fachmedien Wiesbaden : $b Imprint: Springer, $c 2021.
300 $a vii, 41 p. : $b ill., digital ; $c 24 cm.
490 1 $a essentials
505 0 $a 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.
520 $a 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.
650 0 $a Forms, Modular. $3 540521
650 1 4 $a Number Theory. $3 891078
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a essentials. $3 3264003
856 4 0 $u https://doi.org/10.1007/978-3-658-34529-7
950 $a Mathematics and Statistics (SpringerNature-11649)