Number Theory in the Spirit of Liouville (eBook, 2010) []
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Number Theory in the Spirit of Liouville

Author: Kenneth S Williams
Publisher: Cambridge : Cambridge University Press, 2010.
Series: London Mathematical Society student texts, no. 76.
Edition/Format:   eBook : Document : EnglishView all editions and formats

The only book entirely devoted to Joseph Liouville's elementary method in number theory, this gentle introduction explains his method in a clear and straightforward manner, including many  Read more...


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Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Kenneth S Williams
ISBN: 9780511751684 0511751680 9781107002531 1107002532 9780521175623 0521175623
OCLC Number: 1170588164
Description: 1 online resource (306 pages)
Contents: Preface; 1. Joseph Liouville (1809-1888); 2. Liouville's ideas in number theory; 3. The arithmetic functions k(n), k*(n), dk,m(n) and Fk(n); 4. The equation i2 + jk = n; 5. An identity of Liouville; 6. A recurrence relation for *(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.
Series Title: London Mathematical Society student texts, no. 76.
Responsibility: Kenneth S. Williams.


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'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.' Mathematical Reviews

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