Video library: G. V. Fedorov, The Riemann-Roch theorem and periodicity of continued fractions in hyperelliptic fields

VIDEO LIBRARY


Conference to the Memory of Anatoly Alekseevitch Karatsuba on Number theory and Applications January 30, 2016 11:05, Dorodnitsyn Computing Centre, Department of Mechanics and Mathematics of Lomonosov Moscow State University., 119991, GSP-1, Moscow, Leninskie Gory, 1, Main Building, Department of Mechanics and Mathematics, 16 floor, Lecture hall 16-10

The Riemann-Roch theorem and periodicity of continued fractions in hyperelliptic fields G. V. Fedorov^ab ^a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics ^b Scientific Research Institute for System Studies of RAS, Moscow
Abstract: Let $L$ - function field of a hyperelliptic curve $C$ defined over an arbitrary perfect field of characteristic different from $2$. The purpose of the report is that using Riemann-Roch theorem we establish a criterion of periodicity of continued fraction expansion of the key elements of $L$ provided that exists the torsion point on a Jacobian of hyperelliptic curve $C$.