Quadratic Number Fields

Franz Lemmermeyer has worked in algebraic number theory and has published several books on the history of number theory, in particular on reciprocity laws.

1. 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 is a wonderful, well-written introduction to modern algebraic number theory that has been made accessible to a broad undergraduate audience through the author's restriction to quadratic number fields. Historically motivated, it shows how algebraic number theory has evolved over time and depicts it as living and breathing, not as a field that became static in the late 19th century." (Benjamin Linowitz, MAA Reviews, November 21, 2023)

"The book is very nicely written and the original style and choices of the topics make it agreeable reading, and might well complement and motivate the study of other classical introductions to the theory of more general number fields." (Alessandro Cobbe, zbMATH 1498.11003, 2022)