Continued fraction expansions of complex numbers with Gaussian and Eisenstein integers

S.G. Dani
Indian Institute of Technology, Mumbai

Date(s) : 19/06/2018   iCal
11 h 00 min - 12 h 00 min

Continued fraction expansions of real numbers have been the subject of much study for over two centuries and have played an important role in many branches of mathematics. Analogous study for complex numbers has received relatively little attention, though it was initiated already in the 1880s by Adolph Hurwitz. In this talk we shall trace the developments and describe some recent results concerning continued fraction expansions of complex numbers, mainly with respect to the rings of Gaussian and Eisenstein integers, and present some applications in Diophantine approximation.


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