000			nam a22 4500
999			_c32501 _d32501
008			230901b xxu||||| |||| 00| 0 eng d
020			_a9783030786519
082			_a512.74 _bLEM
100			_aLemmermeyer, Franz
245			_aQuadratic number fields
260			_bSpringer, _c2021 _aCham :
300			_axi, 343 p. ; _bill., _c24 cm
365			_b34.99 _cEUR _d94.90
490			_aSpringer undergraduate mathematics series
504			_aIncludes bibliographical references and index.
520			_aThis 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 fields
650			_aAlgebraic bodies
650			_aQuadratic bodies
942			_2ddc _cBK