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

2015/07/21 by Bryant Davis, Rebecca Kotsonis, Jeremy Rouse · 1 citation
Mathematics · #math.NT #msc:11G05

paper · pdf

published as Proc. Amer. Math. Soc. Ser. B 4 (2017), 5-20 · 15 pages

arxiv created 2015/07/21 · arxiv updated 2018/01/22

Abstract

The Somos-5 sequence is defined by a₀ = a₁ = a₂ = a₃ = a₄ = 1 and a_m = \fraca_m-1 a_m-4 + a_m-2 a_m-3a_m-5 for m ≥ 5. We relate the arithmetic of the Somos-5 sequence to the elliptic curve E : y² + xy = x³ + x² - 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 (5087)/(10752).

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