國立虎尾科技大學 |

Modular Forms = Fundamental Tools of Mathematics /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Modular Forms/ by Claudia Alfes-Neumann.
其他題名:	Fundamental Tools of Mathematics /
作者:	Alfes-Neumann, Claudia.
面頁冊數:	VIII, 41 p. 8 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Number Theory. -
電子資源:	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. - 1st ed. 2021. - VIII, 41 p. 8 illus.online resource. - Springer essentials,2731-3115. - Springer 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:

672023
Number Theory.

LC Class. No.: QA241-247.5

Dewey Class. No.: 512.7

Modular Forms = Fundamental Tools of Mathematics /
LDR:03418nam a22003975i 4500 001 1056033
003 DE-He213
005 20211011100526.0
007 cr nn 008mamaa
008 220103s2021 gw | s |||| 0|eng d
020 $a 9783658345297 $9 978-3-658-34529-7
024 7 $a 10.1007/978-3-658-34529-7 $2 doi
035 $a 978-3-658-34529-7
050 4 $a QA241-247.5
072 7 $a PBH $2 bicssc
072 7 $a MAT022000 $2 bisacsh
072 7 $a PBH $2 thema
082 0 4 $a 512.7 $2 23
100 1 $a Alfes-Neumann, Claudia. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1323673
245 1 0 $a Modular Forms $h [electronic resource] : $b Fundamental Tools of Mathematics / $c by Claudia Alfes-Neumann.
250 $a 1st ed. 2021.
264 1 $a Wiesbaden : $b Springer Fachmedien Wiesbaden : $b Imprint: Springer, $c 2021.
300 $a VIII, 41 p. 8 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Springer essentials, $x 2731-3115
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 1 4 $a Number Theory. $3 672023
650 0 $a Number theory. $3 527883
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783658345280
776 0 8 $i Printed edition: $z 9783658345303
830 0 $a Springer essentials, $x 2731-3115 $3 1350387
856 4 0 $u https://doi.org/10.1007/978-3-658-34529-7
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)