Publication: On the product of translated division polynomials and somos sequences
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Date
2023-09-01
Authors
Authors
Gezer, Betül
Bizim, Osman
Journal Title
Journal ISSN
Volume Title
Publisher
Wydawnictwo Naukowe Uam
Abstract
We consider the product sequences of the sequences (psi n(P)), (phi n(P)), and (omega n(P)) (n is an element of N) of values of the translated division polynomials of an elliptic curve E/K evaluated at a point P is an element of E(K)2. We prove that these sequences are purely periodic when K is a finite field. Then we use p-adic properties of these sequences to obtain p-adic convergence of product of the Somos 4 and Somos 5 sequences.
Description
Keywords
Elliptic nets, Periodicity, Elliptic curves, Translated division polynomials, Somos sequences, Mathematics