On a class of periodic elements in hyperelliptic fields defined by polynomials of odd degree
https://doi.org/10.22405/2226-8383-2024-25-4-147-153
Abstract
For an arbitrary odd-degree polynomial 𝑓 over an arbitrary field of algebraic numbers K, the class of always quasiperiodic elements in K((𝑥)) of the form 𝑣+𝑤√𝑓/𝑢 , where 𝑣,𝑤, 𝑢 ∈ K[𝑥], in the hyperelliptic field K(𝑥)(√𝑓), has been determined. This class is characterized by certain relationships involving the polynomials 𝑢, 𝑣,𝑤, and 𝑓, as well as their degrees. The class is guaranteed to be nonempty if at least one quasiperiodic element exists in the hyperelliptic field.
Furthermore, a specific subclass of always periodic elements has been identified within this broader class.
About the Author
Maxim Maximovich Petrunin
Scientific Research Institute of System Analysis
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
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Review
For citations:
Petrunin M.M. On a class of periodic elements in hyperelliptic fields defined by polynomials of odd degree. Chebyshevskii Sbornik. 2024;25(4):147-153. (In Russ.) https://doi.org/10.22405/2226-8383-2024-25-4-147-153
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