03058nam 22005175 450 991050300460332120260203132449.0303078652810.1007/978-3-030-78652-6(CKB)4940000000612108(MiAaPQ)EBC6729690(Au-PeEL)EBL6729690(OCoLC)1268683959(PPN)258052392(DE-He213)978-3-030-78652-6(EXLCZ)99494000000061210820210918d2021 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierQuadratic Number Fields /by Franz Lemmermeyer1st ed. 2021.Cham :Springer International Publishing :Imprint: Springer,2021.XI, 343 p. ; 24 cmSpringer Undergraduate Mathematics Series,2197-41443-030-78651-X Incluye bibliografía e índice1. Prehistory -- 2 Quadratic Number Fields -- 3 The Modularity Theorem -- 4 Divisibility in Integral Domains -- 5 Arithmetic in some Quadratic Number Fields -- 6 Ideals in Quadratic Number Fields -- 7 The Pell Equation -- 8 Catalan's Equation -- 9 Ambiguous Ideal Classes and Quadratic Reciprocity -- 10 Quadratic Gauss Sums -- A Computing with Pari and Sage -- B Solutions -- Bibliography -- Name Index -- Subject Index.This 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 elementarynumber theory and abstract algebra, Quadratic Number Fields offers an engaging first course in algebraic number theory, suitable for upper undergraduate students.Springer Undergraduate Mathematics Series,2197-4144Number theoryNumber TheoryNumber theory.Number Theory.512.7Lemmermeyer Franz1962-724791MiAaPQMiAaPQMiAaPQUMA.CNCBOOK9910503004603321Quadratic Number Fields1897411UNINA