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Number Theory in the Spirit of Liouville

Table of Contents

Preface
1. Joseph Liouville (1809–1888)
2. Liouville's ideas in number theory
3. The arithmetic functions σk(n), σk*(n), dk,m(n) and Fk(n)
4. The equation i2 + jk = n
5. An identity of Liouville
6. A recurrence relation for σ*(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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