From the 1 of 8 linked papers with an AI index.
8 papers
Euclidean Rings
Franz Lemmermeyer
This is the text of my diploma thesis on Euclidean Rings from 1989, along with an English translation. Its main result is the generalization of Lenstra's idead of exceptional seque…
Kuroda's Class Number Formula
Franz Lemmermeyer
The paper provides an algebraic (non‑analytic) proof of the class number formula specifically for biquadratic extensions of number fields.
Vieta jumping and small norms in quadratic number fields
Franz Lemmermeyer
In this article we explain the connection between the famous problemfrom the IMO 1988 and elements of small norms in quadratic number fields with parametrized units.
Dirichlet's Lemma in Number Fields
Franz Lemmermeyer
Dirichlet's Lemma states that every primitive quadratic Dirichlet character can be written in the form for a suitable quadratic discriminant . In this…
Gauss and p-adic numbers
Franz Lemmermeyer
In his notebooks, Gauss recorded various calculations with "infinite congruences". These infinite congruences are p-adic numbers; Gauss computes a square root of in the -ad…
Octic Hilbert 2-class fields of real quadratic fields with discriminant 8p
Franz Lemmermeyer
In this article we explain how to construct cyclic octic unramfied extensions of the real quadratic number field , where is a pri…