國立虎尾科技大學 |

The power of q = a personal journey /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	The power of q/ by Michael D. Hirschhorn.
其他題名:	a personal journey /
作者:	Hirschhorn, Michael D.
出版者:	Cham :Springer International Publishing : : 2017.,
面頁冊數:	xxii, 415 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	q-series. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-57762-3
ISBN:	9783319577623

The power of q = a personal journey /
Hirschhorn, Michael D.

The power of qa personal journey /[electronic resource] :by Michael D. Hirschhorn. - Cham :Springer International Publishing :2017. - xxii, 415 p. :ill., digital ;24 cm. - Developments in mathematics,v.491389-2177 ;. - Developments in mathematics ;v.20..

This unique book explores the world of q, known technically as basic hypergeometric series, and represents the author's personal and life-long study--inspired by Ramanujan--of aspects of this broad topic. While the level of mathematical sophistication is graduated, the book is designed to appeal to advanced undergraduates as well as researchers in the field. The principal aims are to demonstrate the power of the methods and the beauty of the results. The book contains novel proofs of many results in the theory of partitions and the theory of representations, as well as associated identities. Though not specifically designed as a textbook, parts of it may be presented in course work; it has many suitable exercises. After an introductory chapter, the power of q-series is demonstrated with proofs of Lagrange's four-squares theorem and Gauss's two-squares theorem. Attention then turns to partitions and Ramanujan's partition congruences. Several proofs of these are given throughout the book. Many chapters are devoted to related and other associated topics. One highlight is a simple proof of an identity of Jacobi with application to string theory. On the way, we come across the Rogers-Ramanujan identities and the Rogers-Ramanujan continued fraction, the famous "forty identities" of Ramanujan, and the representation results of Jacobi, Dirichlet and Lorenz, not to mention many other interesting and beautiful results. We also meet a challenge of D.H. Lehmer to give a formula for the number of partitions of a number into four squares, prove a "mysterious" partition theorem of H. Farkas and prove a conjecture of R.Wm. Gosper "which even Erdos couldn't do." The book concludes with a look at Ramanujan's remarkable tau function.

ISBN: 9783319577623

Standard No.: 10.1007/978-3-319-57762-3doiSubjects--Topical Terms:

815097
q-series.

LC Class. No.: QA295

Dewey Class. No.: 515.243

The power of q = a personal journey /
LDR:02713nam a2200313 a 4500 001 923748
003 DE-He213
005 20180319112202.0
006 m d
007 cr nn 008maaau
008 190625s2017 gw s 0 eng d
020 $a 9783319577623 $q (electronic bk.)
020 $a 9783319577616 $q (paper)
024 7 $a 10.1007/978-3-319-57762-3 $2 doi
035 $a 978-3-319-57762-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA295
072 7 $a PBH $2 bicssc
072 7 $a MAT022000 $2 bisacsh
082 0 4 $a 515.243 $2 23
090 $a QA295 $b .H669 2017
100 1 $a Hirschhorn, Michael D. $3 1200311
245 1 4 $a The power of q $h [electronic resource] : $b a personal journey / $c by Michael D. Hirschhorn.
260 $a Cham : $c 2017. $b Springer International Publishing : $b Imprint: Springer,
300 $a xxii, 415 p. : $b ill., digital ; $c 24 cm.
490 1 $a Developments in mathematics, $x 1389-2177 ; $v v.49
520 $a This unique book explores the world of q, known technically as basic hypergeometric series, and represents the author's personal and life-long study--inspired by Ramanujan--of aspects of this broad topic. While the level of mathematical sophistication is graduated, the book is designed to appeal to advanced undergraduates as well as researchers in the field. The principal aims are to demonstrate the power of the methods and the beauty of the results. The book contains novel proofs of many results in the theory of partitions and the theory of representations, as well as associated identities. Though not specifically designed as a textbook, parts of it may be presented in course work; it has many suitable exercises. After an introductory chapter, the power of q-series is demonstrated with proofs of Lagrange's four-squares theorem and Gauss's two-squares theorem. Attention then turns to partitions and Ramanujan's partition congruences. Several proofs of these are given throughout the book. Many chapters are devoted to related and other associated topics. One highlight is a simple proof of an identity of Jacobi with application to string theory. On the way, we come across the Rogers-Ramanujan identities and the Rogers-Ramanujan continued fraction, the famous "forty identities" of Ramanujan, and the representation results of Jacobi, Dirichlet and Lorenz, not to mention many other interesting and beautiful results. We also meet a challenge of D.H. Lehmer to give a formula for the number of partitions of a number into four squares, prove a "mysterious" partition theorem of H. Farkas and prove a conjecture of R.Wm. Gosper "which even Erdos couldn't do." The book concludes with a look at Ramanujan's remarkable tau function.
650 0 $a q-series. $3 815097
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Number Theory. $3 672023
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Developments in mathematics ; $v v.20. $3 881577
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-57762-3
950 $a Mathematics and Statistics (Springer-11649)