The Resource The Power of q : A Personal Journey, by Michael D. Hirschhorn, (electronic resource)
The Power of q : A Personal Journey, by Michael D. Hirschhorn, (electronic resource)
Resource Information
The item The Power of q : A Personal Journey, by Michael D. Hirschhorn, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item The Power of q : A Personal Journey, by Michael D. Hirschhorn, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 This unique book explores the world of q, known technically as basic hypergeometric series, and represents the author’s personal and lifelong 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 qseries is demonstrated with proofs of Lagrange’s foursquares theorem and Gauss’s twosquares 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 Erdős couldn’t do.” The book concludes with a look at Ramanujan’s remarkable tau function.
 Language
 eng
 Extent
 1 online resource (XXII, 415 pages)
 Contents

 Foreword
 Preface
 1. Introduction
 2. Jacobi's twosquares and foursquares theorems
 3. Ramanujan's partition congruences
 4. Ramanujan's partition congruences— a uniform proof
 5. Ramanujan's "most beautiful identity"
 6. Ramanujan's partition congruences for powers of 5
 7. Ramanujan's partition congruences for powers of 7
 8. Ramanujan's 5dissection of Euler's product
 9. A "difficult and deep" identity of Ramanujan
 10. The quintuple product identity
 11. Winquist's identity
 12. The crank of a partition
 13. Two more proofs of p(11n + 6) ≡ 0 (mod 11), and more
 14. Partitions where even parts come in two colours
 15. The Rogers–Ramanujan identities and the Rogers–Ramanujan continued fraction
 16. The series expansion of the Rogers–Ramanujan continued fraction
 17. The 2 and 4dissections of Ramanujan’s continued fraction and its reciprocal
 18. The series expansion of the RamanujanGollnitzGordon continued fraction and its reciprocal
 19. Jacobi’s “aequatio identica satis abstrusa”
 20. Two modular equations
 21. A letter from Fitzroy House
 22. The cubic functions of Borwein, Borwein and Garvan
 23. Some classical results on representations
 24. Further classical results on representations
 25. Further results on representations
 26. Even more representation results
 27. Representation results and Lambert series
 28. The Jordan–Kronecker identity
 29. Melham’s identities
 30. Partitions into four squares
 31. Partitions into four distinct squares of equal parity
 32. Partitions with odd parts distinct
 33. Partitions with even parts distinct
 34. Some identities involving phi(q) and psi(q)
 35. Some useful parametrisations
 36. Overpartitions
 37. Bipartitions with odd parts distinct
 38. Overcubic partitions
 39. Generalised Frobenius partitions
 40. Some modular equations of Ramanujan
 41. Identities involving k = qR(q)R(q2)2
 42. Identities involving v=q1/2(q,q7;q8)infinity/(q3,q5;q8)infinity
 43. Ramanujan's tau function
 Appendix
 Index
 Isbn
 9783319577623
 Label
 The Power of q : A Personal Journey
 Title
 The Power of q
 Title remainder
 A Personal Journey
 Statement of responsibility
 by Michael D. Hirschhorn
 Language
 eng
 Summary
 This unique book explores the world of q, known technically as basic hypergeometric series, and represents the author’s personal and lifelong 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 qseries is demonstrated with proofs of Lagrange’s foursquares theorem and Gauss’s twosquares 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 Erdős couldn’t do.” The book concludes with a look at Ramanujan’s remarkable tau function.
 Assigning source
 Provided by publisher
 http://library.link/vocab/creatorName
 Hirschhorn, Michael D
 Image bit depth
 0
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement

 Springer eBooks
 Developments in Mathematics,
 Series volume
 49
 http://library.link/vocab/subjectName

 Mathematics
 Number theory
 Label
 The Power of q : A Personal Journey, by Michael D. Hirschhorn, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Foreword  Preface  1. Introduction  2. Jacobi's twosquares and foursquares theorems  3. Ramanujan's partition congruences  4. Ramanujan's partition congruences— a uniform proof  5. Ramanujan's "most beautiful identity"  6. Ramanujan's partition congruences for powers of 5  7. Ramanujan's partition congruences for powers of 7  8. Ramanujan's 5dissection of Euler's product  9. A "difficult and deep" identity of Ramanujan  10. The quintuple product identity  11. Winquist's identity  12. The crank of a partition  13. Two more proofs of p(11n + 6) ≡ 0 (mod 11), and more  14. Partitions where even parts come in two colours  15. The Rogers–Ramanujan identities and the Rogers–Ramanujan continued fraction  16. The series expansion of the Rogers–Ramanujan continued fraction  17. The 2 and 4dissections of Ramanujan’s continued fraction and its reciprocal  18. The series expansion of the RamanujanGollnitzGordon continued fraction and its reciprocal  19. Jacobi’s “aequatio identica satis abstrusa”  20. Two modular equations  21. A letter from Fitzroy House  22. The cubic functions of Borwein, Borwein and Garvan  23. Some classical results on representations  24. Further classical results on representations  25. Further results on representations  26. Even more representation results  27. Representation results and Lambert series  28. The Jordan–Kronecker identity  29. Melham’s identities  30. Partitions into four squares  31. Partitions into four distinct squares of equal parity  32. Partitions with odd parts distinct  33. Partitions with even parts distinct  34. Some identities involving phi(q) and psi(q)  35. Some useful parametrisations  36. Overpartitions  37. Bipartitions with odd parts distinct  38. Overcubic partitions  39. Generalised Frobenius partitions  40. Some modular equations of Ramanujan  41. Identities involving k = qR(q)R(q2)2  42. Identities involving v=q1/2(q,q7;q8)infinity/(q3,q5;q8)infinity  43. Ramanujan's tau function  Appendix  Index
 Control code
 9783319577623
 Dimensions
 unknown
 Extent
 1 online resource (XXII, 415 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319577623
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319577623
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1000451420
 Label
 The Power of q : A Personal Journey, by Michael D. Hirschhorn, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Foreword  Preface  1. Introduction  2. Jacobi's twosquares and foursquares theorems  3. Ramanujan's partition congruences  4. Ramanujan's partition congruences— a uniform proof  5. Ramanujan's "most beautiful identity"  6. Ramanujan's partition congruences for powers of 5  7. Ramanujan's partition congruences for powers of 7  8. Ramanujan's 5dissection of Euler's product  9. A "difficult and deep" identity of Ramanujan  10. The quintuple product identity  11. Winquist's identity  12. The crank of a partition  13. Two more proofs of p(11n + 6) ≡ 0 (mod 11), and more  14. Partitions where even parts come in two colours  15. The Rogers–Ramanujan identities and the Rogers–Ramanujan continued fraction  16. The series expansion of the Rogers–Ramanujan continued fraction  17. The 2 and 4dissections of Ramanujan’s continued fraction and its reciprocal  18. The series expansion of the RamanujanGollnitzGordon continued fraction and its reciprocal  19. Jacobi’s “aequatio identica satis abstrusa”  20. Two modular equations  21. A letter from Fitzroy House  22. The cubic functions of Borwein, Borwein and Garvan  23. Some classical results on representations  24. Further classical results on representations  25. Further results on representations  26. Even more representation results  27. Representation results and Lambert series  28. The Jordan–Kronecker identity  29. Melham’s identities  30. Partitions into four squares  31. Partitions into four distinct squares of equal parity  32. Partitions with odd parts distinct  33. Partitions with even parts distinct  34. Some identities involving phi(q) and psi(q)  35. Some useful parametrisations  36. Overpartitions  37. Bipartitions with odd parts distinct  38. Overcubic partitions  39. Generalised Frobenius partitions  40. Some modular equations of Ramanujan  41. Identities involving k = qR(q)R(q2)2  42. Identities involving v=q1/2(q,q7;q8)infinity/(q3,q5;q8)infinity  43. Ramanujan's tau function  Appendix  Index
 Control code
 9783319577623
 Dimensions
 unknown
 Extent
 1 online resource (XXII, 415 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319577623
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319577623
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1000451420
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/ThePowerofqAPersonalJourneybyMichael/d8YZBDNkI54/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/ThePowerofqAPersonalJourneybyMichael/d8YZBDNkI54/">The Power of q : A Personal Journey, by Michael D. Hirschhorn, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>