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Jordan totient quotients. / Moree, Pieter; Saad Eddin, Sumaia; Sedunova, Alisa; Suzuki, Yuta.

In: Journal of Number Theory, Vol. 209, 04.2020, p. 147-166.

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

Harvard

Moree, P, Saad Eddin, S, Sedunova, A & Suzuki, Y 2020, 'Jordan totient quotients', Journal of Number Theory, vol. 209, pp. 147-166. https://doi.org/10.1016/j.jnt.2019.08.014

APA

Moree, P., Saad Eddin, S., Sedunova, A., & Suzuki, Y. (2020). Jordan totient quotients. Journal of Number Theory, 209, 147-166. https://doi.org/10.1016/j.jnt.2019.08.014

Vancouver

Moree P, Saad Eddin S, Sedunova A, Suzuki Y. Jordan totient quotients. Journal of Number Theory. 2020 Apr;209:147-166. https://doi.org/10.1016/j.jnt.2019.08.014

Author

Moree, Pieter ; Saad Eddin, Sumaia ; Sedunova, Alisa ; Suzuki, Yuta. / Jordan totient quotients. In: Journal of Number Theory. 2020 ; Vol. 209. pp. 147-166.

BibTeX

@article{478c9932ec074cba9749d2e6e44a4a46,
title = "Jordan totient quotients",
abstract = "The Jordan totient Jk(n) can be defined by Jk(n)=nk∏p|n(1−p−k). In this paper, we study the average behavior of fractions P/Q of two products P and Q of Jordan totients, which we call Jordan totient quotients. To this end, we describe two general and ready-to-use methods that allow one to deal with a larger class of totient functions. The first one is elementary and the second one uses an advanced method due to Balakrishnan and P{\'e}termann. As an application, we determine the average behavior of the Jordan totient quotient, the kth normalized derivative of the nth cyclotomic polynomial Φn(z) at z=1, the second normalized derivative of the nth cyclotomic polynomial Φn(z) at z=−1, and the average order of the Schwarzian derivative of Φn(z) at z=1.",
keywords = "Cyclotomic polynomial, Jordan totient, Jordan totient quotient",
author = "Pieter Moree and {Saad Eddin}, Sumaia and Alisa Sedunova and Yuta Suzuki",
year = "2020",
month = apr,
doi = "10.1016/j.jnt.2019.08.014",
language = "English",
volume = "209",
pages = "147--166",
journal = "Journal of Number Theory",
issn = "0022-314X",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Jordan totient quotients

AU - Moree, Pieter

AU - Saad Eddin, Sumaia

AU - Sedunova, Alisa

AU - Suzuki, Yuta

PY - 2020/4

Y1 - 2020/4

N2 - The Jordan totient Jk(n) can be defined by Jk(n)=nk∏p|n(1−p−k). In this paper, we study the average behavior of fractions P/Q of two products P and Q of Jordan totients, which we call Jordan totient quotients. To this end, we describe two general and ready-to-use methods that allow one to deal with a larger class of totient functions. The first one is elementary and the second one uses an advanced method due to Balakrishnan and Pétermann. As an application, we determine the average behavior of the Jordan totient quotient, the kth normalized derivative of the nth cyclotomic polynomial Φn(z) at z=1, the second normalized derivative of the nth cyclotomic polynomial Φn(z) at z=−1, and the average order of the Schwarzian derivative of Φn(z) at z=1.

AB - The Jordan totient Jk(n) can be defined by Jk(n)=nk∏p|n(1−p−k). In this paper, we study the average behavior of fractions P/Q of two products P and Q of Jordan totients, which we call Jordan totient quotients. To this end, we describe two general and ready-to-use methods that allow one to deal with a larger class of totient functions. The first one is elementary and the second one uses an advanced method due to Balakrishnan and Pétermann. As an application, we determine the average behavior of the Jordan totient quotient, the kth normalized derivative of the nth cyclotomic polynomial Φn(z) at z=1, the second normalized derivative of the nth cyclotomic polynomial Φn(z) at z=−1, and the average order of the Schwarzian derivative of Φn(z) at z=1.

KW - Cyclotomic polynomial

KW - Jordan totient

KW - Jordan totient quotient

UR - http://www.scopus.com/inward/record.url?scp=85072301195&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/jordan-totient-quotients

UR - https://www.mendeley.com/catalogue/ba559a1a-5004-3996-866e-91123a121386/

U2 - 10.1016/j.jnt.2019.08.014

DO - 10.1016/j.jnt.2019.08.014

M3 - Article

AN - SCOPUS:85072301195

VL - 209

SP - 147

EP - 166

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

ER -

ID: 49819079