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Constrained ternary integers

MPS-Authors
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Luca,  Florian
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons235837

Moree,  Pieter
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons236174

Sedunova,  Alisa
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

http://dx.doi.org/10.1142/S1793042119500210
(Publisher version)

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Citation

Luca, F., Moree, P., Osburn, R., Saad Eddin, S., & Sedunova, A. (2019). Constrained ternary integers. International Journal of Number Theory, 15(2), 407-431. doi:10.1142/S1793042119500210.


Cite as: https://hdl.handle.net/21.11116/0000-0004-4062-5
Abstract
An integer n is said to be ternary if it is composed of three distinct odd primes. In this paper, we asymptotically count the number of ternary integers n≤x with the constituent primes satisfying various constraints. We apply our results to the study of the simplest class of (inverse) cyclotomic polynomials that can have coefficients that are greater than 1 in absolute value, namely to the nth (inverse) cyclotomic polynomials with ternary n. We show, for example, that the corrected Sister Beiter conjecture is true for a fraction ≥0.925 of ternary integers.