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The density of primes dividing a term in the Somos-5 sequence

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abstract
The Somos-5 sequence is defined by $ a_{0} = a_{1} = a_{2} = a_{3} = a_{4} = 1$ and $ a_{m} = \frac {a_{m-1} a_{m-4} + a_{m-2} a_{m-3}}{a_{m-5}}$ for $ m \geq 5$. We relate the arithmetic of the Somos-5 sequence to the elliptic curve $ E : y^{2} + xy = x^{3} + x^{2} - 2x$ and use properties of Galois representations attached to $ E$ to prove the density of primes $ p$ dividing some term in the Somos-5 sequence is equal to $ \frac {5087}{10752}$.
subject
mathematics
Somos-5 sequence
contributor
Davis, B. (author)
Kotsonis, R. (author)
Rouse, J. (author)
date
2020-02-25T20:45:39Z (accessioned)
2020-02-25T20:45:39Z (available)
8/3/17 (issued)
identifier
Davis, B., Kotsonis, R., & Rouse, J. (2017). The density of primes dividing a term in the Somos-5 sequence. Proceedings of the American Mathematical Society, Series B, 4(2), 5-20. (citation)
https://doi.org/10.1090/bproc/26 (doi)
http://hdl.handle.net/10339/95995 (uri)
language
en (iso)
publisher
American Mathematical Society
rights
https://creativecommons.org/licenses/by-nc-sa/3.0/ (uri)
source
Proceedings of the American Mathematical Society
title
The density of primes dividing a term in the Somos-5 sequence
type
Article

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