02271nam a22003498a 4500 CR9780511751684 UkCbUP 20180107143412.0 m|||||o||d|||||||| cr|||||||||||| 100420s2010||||enk s ||1 0|eng|d 9780511751684 (ebook) 9781107002531 (hardback) 9780521175623 (paperback) UkCbUP UkCbUP rda QA241 .W625 2010 512.7/2 22 Williams, Kenneth S., author. Number Theory in the Spirit of Liouville / [electronic resource] Kenneth S. Williams. Cambridge : Cambridge University Press, 2010. 1 online resource (306 pages) : digital, PDF file(s). text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society Student Texts ; no. 76 Title from publisher's bibliographic system (viewed on 09 Oct 2015). 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 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. Number theory Print version: 9781107002531 London Mathematical Society Student Texts ; no. 76. http://dx.doi.org/10.1017/CBO9780511751684 Cambridge Books Online 236501 236501