Quadratic Number Theory: An Invitation to Algebraic Methods in the Higher Arithmetic

Quadratic Number Theory: An Invitation to Algebraic Methods in the Higher Arithmetic

Description

Quadratic Number Theory is an introduction to algebraic number theory for readers with a moderate knowledge of elementary number theory and some familiarity with the terminology of abstract algebra. By restricting attention to questions about squares the author achieves the dual goals of making the presentation accessible to undergraduates and reflecting the historical roots of the subject. The representation of integers by quadratic forms is emphasized throughout the text.

Lehman introduces an innovative notation for ideals of a quadratic domain that greatly facilitates computation and he uses this to particular effect. The text has an unusual focus on actual computation. This focus, and this notation, serve the author's historical purpose as well; ideals can be seen as number-like objects, as Kummer and Dedekind conceived of them. The notation can be adapted to quadratic forms and provides insight into the connection between quadratic forms and ideals. The computation of class groups and continued fraction representations are featured—the author's notation makes these computations particularly illuminating.

ISBN

978-1-4704-4737-3

Publication Date

2019

Publisher

MAA Press: An Imprint of the American Mathematical Society

City

Providence (RI)

Keywords

Quadratic number theory, Algebraic number theory, Quadratic forms

Disciplines

Algebra | Mathematics | Number Theory

Quadratic Number Theory: An Invitation to Algebraic Methods in the Higher Arithmetic

Share

 
COinS