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Speaker:
Hohto Bekki
Zugehörigkeit:
MPIM
Datum:
Mit, 07/03/2018 - 16:30 - 17:30
Location:
MPIM Lecture Hall
Parent event:
Number theory lunch seminar In this talk, we present some generalizations of Lagrange's periodicity theorem in the classical theory of continued fractions. The main idea is to use a geometric interpretation of the classical theory in terms of closed geodesics on the modular curve. As a result, for an extension F/F' of number fields with rank one relative unit group, we construct a geodesic multi-dimensional continued fraction algorithm to "expand'' a basis of F over the rationals, and prove its periodicity. Furthermore, we show that the periods describe the relative unit group. By extending the above argument adelically, we also obtain a p-adelic continued fraction algorithm and its periodicity for imaginary quadratic irrationals.
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