20 citations · 45 across the 7 of their papers we have counts for
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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.