Number theory in the spirit of Liouville:
Joseph Liouville is recognised as one of the great mathematicians of the nineteenth century, and one of his greatest achievements was the introduction of a powerful new method into elementary number theory. This book provides a gentle introduction to this method, explaining it in a clear and straigh...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2010
|
| Series: | London Mathematical Society student texts
76 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | Joseph Liouville is recognised as one of the great mathematicians of the nineteenth century, and one of his greatest achievements was the introduction of a powerful new method into elementary number theory. This book provides a gentle introduction to this method, explaining it in a clear and straightforward manner. The many applications provided include applications to sums of squares, sums of triangular numbers, recurrence relations for divisor functions, convolution sums involving the divisor functions, and many others. All of the topics discussed have a rich history dating back to Euler, Jacobi, Dirichlet, Ramanujan and others, and they continue to be the subject of current mathematical research. Williams places the results in their historical and contemporary contexts, making the connection between Liouville's ideas and modern theory. This is the only book in English entirely devoted to the subject and is thus an extremely valuable resource for both students and researchers alike |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 Online-Ressource (xvii, 287 Seiten) |
| ISBN: | 9780511751684 |
| DOI: | 10.1017/CBO9780511751684 |
Staff View
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| 505 | 8 | |a Machine generated contents note: Preface; 1. Joseph Liouville (1809-1888); 2. Liouville's ideas in number theory; 3. The arithmetic functions [sigma]k(n), [sigma]k*(n), dk,m(n) and Fk(n); 4. The equation i2 + jk = n; 5. An identity of Liouville; 6. A recurrence relation for [sigma]*(n); 7. The Girard-Fermat theorem; 8. A second identity of Liouville; 9. Sums of two, four and six squares; 10. A third identity of Liouville; 11. Jacobi's four squares formula; 12. Besge's formula; 13. An identity of Huard, Ou, Spearman and Williams; 14. Four elementary arithmetic formulae; 15. Some twisted convolution sums; 16. Sums of two, four, six and eight triangular numbers; 17. Sums of integers of the form x2+xy+y2; 18. Representations by x2+y2+z2+2t2, x2+y2+2z2+2t2 and x2+2y2+2z2+2t2; 19. Sums of eight and twelve squares; 20. Concluding remarks; References; Index | |
| 520 | |a Joseph Liouville is recognised as one of the great mathematicians of the nineteenth century, and one of his greatest achievements was the introduction of a powerful new method into elementary number theory. This book provides a gentle introduction to this method, explaining it in a clear and straightforward manner. The many applications provided include applications to sums of squares, sums of triangular numbers, recurrence relations for divisor functions, convolution sums involving the divisor functions, and many others. All of the topics discussed have a rich history dating back to Euler, Jacobi, Dirichlet, Ramanujan and others, and they continue to be the subject of current mathematical research. Williams places the results in their historical and contemporary contexts, making the connection between Liouville's ideas and modern theory. This is the only book in English entirely devoted to the subject and is thus an extremely valuable resource for both students and researchers alike | ||
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Record in the Search Index
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| any_adam_object | |
| author | Williams, Kenneth S. 1940- |
| author_GND | (DE-588)132012030 |
| author_facet | Williams, Kenneth S. 1940- |
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| contents | Machine generated contents note: Preface; 1. Joseph Liouville (1809-1888); 2. Liouville's ideas in number theory; 3. The arithmetic functions [sigma]k(n), [sigma]k*(n), dk,m(n) and Fk(n); 4. The equation i2 + jk = n; 5. An identity of Liouville; 6. A recurrence relation for [sigma]*(n); 7. The Girard-Fermat theorem; 8. A second identity of Liouville; 9. Sums of two, four and six squares; 10. A third identity of Liouville; 11. Jacobi's four squares formula; 12. Besge's formula; 13. An identity of Huard, Ou, Spearman and Williams; 14. Four elementary arithmetic formulae; 15. Some twisted convolution sums; 16. Sums of two, four, six and eight triangular numbers; 17. Sums of integers of the form x2+xy+y2; 18. Representations by x2+y2+z2+2t2, x2+y2+2z2+2t2 and x2+2y2+2z2+2t2; 19. Sums of eight and twelve squares; 20. Concluding remarks; References; Index |
| ctrlnum | (ZDB-20-CBO)CR9780511751684 (OCoLC)907964345 (DE-599)BVBBV043941027 |
| dewey-full | 512.7/2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7/2 |
| dewey-search | 512.7/2 |
| dewey-sort | 3512.7 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511751684 |
| format | Electronic eBook |
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| id | DE-604.BV043941027 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:14Z |
| institution | BVB |
| isbn | 9780511751684 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029349996 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (xvii, 287 Seiten) |
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| publishDate | 2010 |
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| spelling | Williams, Kenneth S. 1940- Verfasser (DE-588)132012030 aut Number theory in the spirit of Liouville Kenneth S. Williams Cambridge Cambridge University Press 2010 1 Online-Ressource (xvii, 287 Seiten) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society student texts 76 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Machine generated contents note: Preface; 1. Joseph Liouville (1809-1888); 2. Liouville's ideas in number theory; 3. The arithmetic functions [sigma]k(n), [sigma]k*(n), dk,m(n) and Fk(n); 4. The equation i2 + jk = n; 5. An identity of Liouville; 6. A recurrence relation for [sigma]*(n); 7. The Girard-Fermat theorem; 8. A second identity of Liouville; 9. Sums of two, four and six squares; 10. A third identity of Liouville; 11. Jacobi's four squares formula; 12. Besge's formula; 13. An identity of Huard, Ou, Spearman and Williams; 14. Four elementary arithmetic formulae; 15. Some twisted convolution sums; 16. Sums of two, four, six and eight triangular numbers; 17. Sums of integers of the form x2+xy+y2; 18. Representations by x2+y2+z2+2t2, x2+y2+2z2+2t2 and x2+2y2+2z2+2t2; 19. Sums of eight and twelve squares; 20. Concluding remarks; References; Index Joseph Liouville is recognised as one of the great mathematicians of the nineteenth century, and one of his greatest achievements was the introduction of a powerful new method into elementary number theory. This book provides a gentle introduction to this method, explaining it in a clear and straightforward manner. The many applications provided include applications to sums of squares, sums of triangular numbers, recurrence relations for divisor functions, convolution sums involving the divisor functions, and many others. All of the topics discussed have a rich history dating back to Euler, Jacobi, Dirichlet, Ramanujan and others, and they continue to be the subject of current mathematical research. Williams places the results in their historical and contemporary contexts, making the connection between Liouville's ideas and modern theory. This is the only book in English entirely devoted to the subject and is thus an extremely valuable resource for both students and researchers alike Liouville, Joseph / 1809-1882 Liouville, Joseph 1809-1882 (DE-588)118938525 gnd rswk-swf Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Liouville, Joseph 1809-1882 (DE-588)118938525 p Zahlentheorie (DE-588)4067277-3 s 1\p DE-604 Erscheint auch als Druck-Ausgabe 978-1-107-00253-1 Erscheint auch als Druck-Ausgabe 978-0-521-17562-3 https://doi.org/10.1017/CBO9780511751684 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Williams, Kenneth S. 1940- Number theory in the spirit of Liouville Machine generated contents note: Preface; 1. Joseph Liouville (1809-1888); 2. Liouville's ideas in number theory; 3. The arithmetic functions [sigma]k(n), [sigma]k*(n), dk,m(n) and Fk(n); 4. The equation i2 + jk = n; 5. An identity of Liouville; 6. A recurrence relation for [sigma]*(n); 7. The Girard-Fermat theorem; 8. A second identity of Liouville; 9. Sums of two, four and six squares; 10. A third identity of Liouville; 11. Jacobi's four squares formula; 12. Besge's formula; 13. An identity of Huard, Ou, Spearman and Williams; 14. Four elementary arithmetic formulae; 15. Some twisted convolution sums; 16. Sums of two, four, six and eight triangular numbers; 17. Sums of integers of the form x2+xy+y2; 18. Representations by x2+y2+z2+2t2, x2+y2+2z2+2t2 and x2+2y2+2z2+2t2; 19. Sums of eight and twelve squares; 20. Concluding remarks; References; Index Liouville, Joseph / 1809-1882 Liouville, Joseph 1809-1882 (DE-588)118938525 gnd Number theory Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)118938525 (DE-588)4067277-3 |
| title | Number theory in the spirit of Liouville |
| title_auth | Number theory in the spirit of Liouville |
| title_exact_search | Number theory in the spirit of Liouville |
| title_full | Number theory in the spirit of Liouville Kenneth S. Williams |
| title_fullStr | Number theory in the spirit of Liouville Kenneth S. Williams |
| title_full_unstemmed | Number theory in the spirit of Liouville Kenneth S. Williams |
| title_short | Number theory in the spirit of Liouville |
| title_sort | number theory in the spirit of liouville |
| topic | Liouville, Joseph / 1809-1882 Liouville, Joseph 1809-1882 (DE-588)118938525 gnd Number theory Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Liouville, Joseph / 1809-1882 Liouville, Joseph 1809-1882 Number theory Zahlentheorie |
| url | https://doi.org/10.1017/CBO9780511751684 |
| work_keys_str_mv | AT williamskenneths numbertheoryinthespiritofliouville |