Cargando…
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 s...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
2010.
|
| Colección: | London Mathematical Society student texts ;
76. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.