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On the Legendre and the Lenstra constants for complex continued fractions introduced by J. Hurwitz

Volume 196 / 2020

Hitoshi Nakada Acta Arithmetica 196 (2020), 269-289 MSC: Primary 11K50; Secondary 37A44, 11J70, 30B70. DOI: 10.4064/aa180713-14-1 Published online: 7 July 2020


We give the explicit value of the Legendre constant associated with the continued fraction expansions for complex numbers defined by J. Hurwitz. To do this, we first give the Lenstra constant of this continued fraction and then show these two constants coincide.


  • Hitoshi NakadaDepartment of Mathematics
    Keio University
    Hiyoshi 3-14-1, Kohoku-ku
    Yokohama, 223-8522 Japan

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