000			01967nam a22002177a 4500
003			OSt
005			20241023110341.0
008			241023b |||||||| |||| 00| 0 hin d
020			_a9783030786519
040			_aNISER LIBRARY _beng _cNISER LIBRARY
041			_aEnglish
082			_a514.162 _bLEM-Q
100			_aLemmermeyer, Franz
245			_aQuadratic number fields
260			_aSwitzerland : _bSpringer, _c2017.
300			_axi, 343p.
490			_aSpringer undergraduate mathematics series _x1615-2085
520			_aThis chapter introduces quadratic number fields, their rings of integers, and the group of rational and integral points on Pell conics and explains the connection with the technique of Vieta jumping. _bThis undergraduate textbook provides an elegant introduction to the arithmetic of quadratic number fields, including many topics not usually covered in books at this level. Quadratic fields offer an introduction to algebraic number theory and some of its central objects: rings of integers, the unit group, ideals and the ideal class group. This textbook provides solid grounding for further study by placing the subject within the greater context of modern algebraic number theory. Going beyond what is usually covered at this level, the book introduces the notion of modularity in the context of quadratic reciprocity, explores the close links between number theory and geometry via Pell conics, and presents applications to Diophantine equations such as the Fermat and Catalan equations as well as elliptic curves. Throughout, the book contains extensive historical comments, numerous exercises (with solutions), and pointers to further study. Assuming a moderate background in elementary number theory and abstract algebra, Quadratic Number Fields offers an engaging first course in algebraic number theory, suitable for upper undergraduate students.
650			_aQuadratic Euclidean and non-Euclidean spaces
942			_2udc _cBK
999			_c35343 _d35343