Publication:
On the product of translated division polynomials and somos sequences

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Date

2023-09-01

Authors

Gezer, Betül
Bizim, Osman

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Wydawnictwo Naukowe Uam

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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.

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Keywords

Elliptic nets, Periodicity, Elliptic curves, Translated division polynomials, Somos sequences, Mathematics

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