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Constrained ternary integers. / Luca, Florian; Moree, Pieter; Osburn, Robert; Eddin, Sumaia Saad; Sedunova, Alisa.

In: International Journal of Number Theory, Vol. 15, No. 2, 2019, p. 407-431.

Research output: Contribution to journal › Article › peer-review

Harvard

Luca, F, Moree, P, Osburn, R, Eddin, SS & Sedunova, A 2019, 'Constrained ternary integers', International Journal of Number Theory, vol. 15, no. 2, pp. 407-431. https://doi.org/10.1142/S1793042119500210

APA

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

Vancouver

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

Author

Luca, Florian ; Moree, Pieter ; Osburn, Robert ; Eddin, Sumaia Saad ; Sedunova, Alisa. / Constrained ternary integers. In: International Journal of Number Theory. 2019 ; Vol. 15, No. 2. pp. 407-431.

BibTeX

@article{d40eeb57fcf54dc380ddb671ccf3835a,
title = "Constrained ternary integers",
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.",
keywords = "cyclotomic polynomials, prime numbers, Ternary integers, FLAT CYCLOTOMIC POLYNOMIALS, BOUNDS, COEFFICIENTS",
author = "Florian Luca and Pieter Moree and Robert Osburn and Eddin, {Sumaia Saad} and Alisa Sedunova",
year = "2019",
doi = "10.1142/S1793042119500210",
language = "English",
volume = "15",
pages = "407--431",
journal = "International Journal of Number Theory",
issn = "1793-0421",
publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",
number = "2",

}

RIS

TY - JOUR

T1 - Constrained ternary integers

AU - Luca, Florian

AU - Moree, Pieter

AU - Osburn, Robert

AU - Eddin, Sumaia Saad

AU - Sedunova, Alisa

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - cyclotomic polynomials

KW - prime numbers

KW - Ternary integers

KW - FLAT CYCLOTOMIC POLYNOMIALS

KW - BOUNDS

KW - COEFFICIENTS

UR - http://www.scopus.com/inward/record.url?scp=85054140068&partnerID=8YFLogxK

U2 - 10.1142/S1793042119500210

DO - 10.1142/S1793042119500210

M3 - Article

AN - SCOPUS:85054140068

VL - 15

SP - 407

EP - 431

JO - International Journal of Number Theory

JF - International Journal of Number Theory

SN - 1793-0421

IS - 2

ER -

ID: 49819176