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Conference to the Memory of Anatoly Alekseevitch Karatsuba on Number theory and Applications
January 30, 2016 11:05–11:30, 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
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The Riemann-Roch theorem and periodicity of continued fractions in hyperelliptic fields
G. V. Fedorovab
a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Scientific Research Institute for System Studies of RAS, Moscow
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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 $C$.
Language: Russian and English
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