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.
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Number theory in the spirit of Liouville by Kenneth S. Williams. ISBN 9780521175623. Published by Cambridge University Press in 2011. Publication and catalogue information, links to buy online and reader comments.
