000			03152nam a22003738i 4500
001			CR9780511751684
003			UkCbUP
005			20200124160225.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			100420s2010||||enk o ||1 0|eng|d
020			_a9780511751684 (ebook)
020			_z9781107002531 (hardback)
020			_z9780521175623 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA241 _b.W625 2010
082	0	0	_a512.7/2 _222
100	1		_aWilliams, Kenneth S., _eauthor.
245	1	0	_aNumber theory in the spirit of Liouville / _cKenneth S. Williams.
264		1	_aCambridge : _bCambridge University Press, _c2010.
300			_a1 online resource (xvii, 287 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aLondon Mathematical Society student texts ; _v76
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	8		_aMachine 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.
520			_aJoseph 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 straightforward manner. The many applications provided include applications to sums of squares, sums of triangular numbers, recurrence relations for divisor functions, convolution sums involving the divisor functions, and many others. All of the topics discussed have a rich history dating back to Euler, Jacobi, Dirichlet, Ramanujan and others, and they continue to be the subject of current mathematical research. Williams places the results in their historical and contemporary contexts, making the connection between Liouville's ideas and modern theory. 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.
650		0	_aNumber theory.
600	1	0	_aLiouville, Joseph, _d1809-1882.
776	0	8	_iPrint version: _z9781107002531
830		0	_aLondon Mathematical Society student texts ; _v76.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511751684
999			_c517102 _d517100