Murty M., Esmonde J. Problems in Algebraic Number Theory

Princeton University Press, 2012, 275 pp., ISBN: 978-0-691-15119-9, Eng., PDF Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics- the Birch and Swinnerton-Dyer Conjecture . The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general...

Springer, 1999. — 599 p. — (Graduate Texts in Mathematics). — ISBN: 0387987274, 9780387987279 Скан. The computation of invariants of algebraic number fields such as integral bases, discriminants, prime decompositions, ideal class groups, and unit groups is important both for its own sake and for its numerous applications, for example, to the solution of Diophantine...

2nd edition. — New York: Springer, 2009. — 610 p. — (Universitext). — ISBN 9780387894850; 978-0-387-89486-7. Number Theory is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included. The book is divided into two parts....

Academic Press, 2007. — 800 pages. Second Edition ISBN: 0123724872 This second edition updates the well-regarded 2001 publication with new short sections on topics like Catalan numbers and their relationship to Pascal's triangle and Mersenne numbers, Pollard rho factorization method, Hoggatt-Hensell identity. Koshy has added a new chapter on continued fractions. The unique...

2nd ed. — Elsevier, 1987. — 748 p. — (North-Holland mathematical library 37). — ISBN: 0-444-70152-4. This volume contains a fairly complete picture of the geometry of numbers, including relations to other branches of mathematics such as analytic number theory, diophantine approximation, coding and numerical analysis. It deals with convex or non-convex bodies and lattices in...

Kluwer Academic Publishers, 2004. 635 p. ISBN: 1-4020-2546-7 (HB) ISBN: 1-4020-2547-5 (e-book) Basic Symbols Basic Notations Perfect Numbers: Old and New Issues; Perspectives ntroduction Some historical facts Even perfect numbers Odd perfect numbers Perfect, multiperfect and multiply perfect numbers Quasiperfect, almost perfect, and pseudoperfect numbers Superperfect and...