Number theory in the spirit of Liouville [EBook] / Kenneth S. Williams.
Number theory in the spirit of Liouville [EBook] / Kenneth S. Williams.
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 straigh...
Personal Name(s):  Williams, Kenneth S., (author) 

Imprint: 
Cambridge :
Cambridge University Press,
2010

Physical Description: 
1 online resource (xvii, 287 pages) 
Note: 
englisch 
ISBN: 
9780521175623 9780511751684 9781107002531 
Series Title: 
London Mathematical Society student texts ;
76 
Subject (LOC):  
Full Text 
Table of Contents:
 Machine generated contents note: Preface; 1. Joseph Liouville (18091888); 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 GirardFermat 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.