20 citations · 45 across the 7 of their papers we have counts for
10 papers
Higher Descent on Pell Conics III. The First 2-Descent
Franz Lemmermeyer
In this articel we describe the first 2-descent on Pell conics, and compute the associated 2-part of the Tate-Shafarevich group.
Higher Descent on Pell Conics I. From Legendre to Selmer
Franz Lemmermeyer
This article deals with the history of certain aspects of the Pell equation X - D y = 4. We briefly discuss explicit units, and then study the history of Legendre's equatio…
Conics - a Poor Man's Elliptic Curves
Franz Lemmermeyer
The aim of this article is to show that the arithmetic of Pell conics admits a description which is completely analogous to that of elliptic curves: there is a theory of 2-descent…
Higher Descent on Pell Conics II. Two Centuries of Missed Opportunities
Franz Lemmermeyer
We discuss the history of attempts to solve the Pell equation using certain auxiliary equations that correspond, in modern terminology, to a second 2-descent.
Imaginary quadratic fields with Cl_2(k) = (2,2,2)
Elliot Benjamin, Franz Lemmermeyer, Chip Snyder
In this article we classify the complex quadratic number fields k with 2-class group of type (2,2,2) whose Hilbert 2-class fields have a 2-class group of rank 2, and then determine…
The development of the princial genus theorem
Franz Lemmermeyer
In this article we sketch the development of the principal genus theorem from its conception by Gauss in the case of binary quadratic forms to the cohomological formulation of the…