Remote Access Proceedings of the American Mathematical Society Series B
Gold Open Access

Proceedings of the American Mathematical Society Series B

ISSN 2330-1511

   
 
 

 

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


Authors: Bryant Davis, Rebecca Kotsonis and Jeremy Rouse
Journal: Proc. Amer. Math. Soc. Ser. B 4 (2017), 5-20
MSC (2010): Primary 11G05; Secondary 11F80
DOI: https://doi.org/10.1090/bproc/26
Published electronically: August 3, 2017
MathSciNet review: 3681974
Full-text PDF Open Access
View in AMS MathViewer New

Abstract | References | Similar Articles | Additional Information

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 $\frac {5087}{10752}$.


References [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society, Series B with MSC (2010): 11G05, 11F80

Retrieve articles in all journals with MSC (2010): 11G05, 11F80


Additional Information

Bryant Davis
Affiliation: Department of Mathematics and Statistics, Wake Forest University, Winston-Salem, North Carolina 27109
Address at time of publication: Department of Statistics, University of Florida, Gainesville, Florida 32611
Email: davibf11@ufl.edu

Rebecca Kotsonis
Affiliation: Department of Mathematics and Statistics, Wake Forest University, Winston-Salem, North Carolina 27109
Email: rkotsonis@uchicago.edu

Jeremy Rouse
Affiliation: Department of Mathematics and Statistics, Wake Forest University, Winston-Salem, North Carolina 27109
MR Author ID: 741123
Email: rouseja@wfu.edu

Received by editor(s): July 21, 2015
Received by editor(s) in revised form: August 26, 2016
Published electronically: August 3, 2017
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2017 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)