Number Theory in the Spirit of Liouville

ISBN-13: 9781107002531 / Angielski / Twarda / 2010 / 287 str.

Kenneth S. Williams

Opis

A gentle introduction to Liouville's powerful method in elementary number theory. Suitable for advanced undergraduate and beginning graduate students.

Recenzje

'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

Spis treści

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.