Some effectivity results for primitive divisors of elliptic divisibility sequences
Verzobio M. 2023. Some effectivity results for primitive divisors of elliptic divisibility sequences. Pacific Journal of Mathematics. 325(2), 331–351.
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Abstract
Let P be a nontorsion point on an elliptic curve defined over a number field K and consider the sequence {Bn}n∈N of the denominators of x(nP). We prove that every term of the sequence of the Bn has a primitive divisor for n greater than an effectively computable constant that we will explicitly compute. This constant will depend only on the model defining the curve.
Publishing Year
Date Published
2023-11-03
Journal Title
Pacific Journal of Mathematics
Publisher
Mathematical Sciences Publishers
Acknowledgement
This paper is part of the author’s PhD thesis at Università of Pisa. Moreover, this
project has received funding from the European Union’s Horizon 2020 research
and innovation programme under the Marie Skłodowska-Curie Grant Agreement
No. 101034413. I thank the referee for many helpful comments.
Volume
325
Issue
2
Page
331-351
eISSN
IST-REx-ID
Cite this
Verzobio M. Some effectivity results for primitive divisors of elliptic divisibility sequences. Pacific Journal of Mathematics. 2023;325(2):331-351. doi:10.2140/pjm.2023.325.331
Verzobio, M. (2023). Some effectivity results for primitive divisors of elliptic divisibility sequences. Pacific Journal of Mathematics. Mathematical Sciences Publishers. https://doi.org/10.2140/pjm.2023.325.331
Verzobio, Matteo. “Some Effectivity Results for Primitive Divisors of Elliptic Divisibility Sequences.” Pacific Journal of Mathematics. Mathematical Sciences Publishers, 2023. https://doi.org/10.2140/pjm.2023.325.331.
M. Verzobio, “Some effectivity results for primitive divisors of elliptic divisibility sequences,” Pacific Journal of Mathematics, vol. 325, no. 2. Mathematical Sciences Publishers, pp. 331–351, 2023.
Verzobio M. 2023. Some effectivity results for primitive divisors of elliptic divisibility sequences. Pacific Journal of Mathematics. 325(2), 331–351.
Verzobio, Matteo. “Some Effectivity Results for Primitive Divisors of Elliptic Divisibility Sequences.” Pacific Journal of Mathematics, vol. 325, no. 2, Mathematical Sciences Publishers, 2023, pp. 331–51, doi:10.2140/pjm.2023.325.331.
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