Number theory in the spirit of Liouville:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge University Press
2011
|
| Schriftenreihe: | London Mathematical Society student texts
76 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | "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"-- Provided by publisher. Includes bibliographical references and index |
| Beschreibung: | XVII, 287 S. 23 cm |
| ISBN: | 9781107002531 9780521175623 |
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Datensatz im Suchindex
| _version_ | 1804149408748535808 |
|---|---|
| adam_text | NUMBER THEORY IN THE SPIRIT OF LIOUVILLE
/ WILLIAMS, KENNETH S.
: 2010
TABLE OF CONTENTS / INHALTSVERZEICHNIS
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.
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
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| illustrated | Not Illustrated |
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| institution | BVB |
| isbn | 9781107002531 9780521175623 |
| language | English |
| lccn | 2010030399 |
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| physical | XVII, 287 S. 23 cm |
| publishDate | 2011 |
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| publisher | Cambridge University Press |
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| series | London Mathematical Society student texts |
| series2 | London Mathematical Society student texts |
| spelling | Williams, Kenneth S. 1940- Verfasser (DE-588)132012030 aut Number theory in the spirit of Liouville Kenneth S. Williams Cambridge [u.a.] Cambridge University Press 2011 XVII, 287 S. 23 cm txt rdacontent n rdamedia nc rdacarrier London Mathematical Society student texts 76 "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"-- Provided by publisher. Includes bibliographical references and index 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 DE-604 London Mathematical Society student texts 76 (DE-604)BV000841726 76 LoC Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025217038&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Williams, Kenneth S. 1940- Number theory in the spirit of Liouville London Mathematical Society student texts 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 Number theory Zahlentheorie |
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