In the paper entitled "Complex continued fractions: early work of the brothers Adolf and Julius Hurwitz" by Nicola M. R. Oswald and Jörn J. Steuding stated that "Moreover, Adolf Hurwitz mentioned that his approach could be used to build up a complex theory of the Pell equation $t^2−Du^2 = 1 $ where $D$ is a given number and solutions $t$ and $u$ are to be complex integers" (page 515). So, from this statement I understood that finding the complex integer solutions of the above equation is the complex theory of Pell equation. Whether I am correct or not? What is the domain of $D$. Where can I find details about this complex theory of Pell equation?
2026-03-29 22:26:45.1774823205
complex theory of Pell equation
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Check out the articles by R. Lakein on "Computation of the Ideal Class Group of Certain Complex Quartic Fields" in Math. Comp. for applications of Hurwitz continued fractions to the computation of units and class numbers. See also the thesis of B. Cijsouw.