On Cyclotomic Polynomial Coefficients
Journal article
Andrica, D. and Bagdasar, O. 2020. On Cyclotomic Polynomial Coefficients. Malaysian Journal of Mathematical Sciences. 14 (3), pp. 289 - 402.
| Authors | Andrica, D. and Bagdasar, O. |
|---|---|
| Abstract | For a positive integer n > 1 the n-th cyclotomic polynomial is defined by (Formula presented) where ς are the primitive n-th roots of unity. These polynomials are known to possess many interesting properties. In this article we establish an integral formula for the coefficients of the cyclotomic polynomial, we then discuss the direct and alternate sums of coefficients, as well as the mid-term of Φn(z). Finally, these results are used in the computation of certain trigonometric integrals. |
| Keywords | alternate sum of coeffi-cients; ; Euler totient function; ; coefficients of cyclotomic polynomials; ; cyclotomic polynomial; ; direct sum of coefficients; ; integral formula; ; mid-term coefficient |
| Year | 2020 |
| Journal | Malaysian Journal of Mathematical Sciences |
| Journal citation | 14 (3), pp. 289 - 402 |
| Publisher | Universiti Putra Malaysia |
| ISSN | 1823-8343 |
| Web address (URL) | https://mjms.upm.edu.my/fullpaper/2020-September-14-3/Andrica,%20D.-389-402.pdf |
| https://publons.com/wos-op/publon/58031784/ | |
| Output status | Published |
| Publication dates | Sep 2020 |
| Publication process dates | |
| Deposited | 25 May 2023 |
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Bagdasar, Ovidiu 2010. Complementary iInequalities involving the Stolarsky Mean. Journal of Inequalities and Applications. https://doi.org/10.1155/2010/492570Concise computer mathematics: tutorials on theory and problems
Bagdasar, Ovidiu 2013. Concise computer mathematics: tutorials on theory and problems. Springer.On the characterization of periodic generalized Horadam sequences
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Bagdasar, Ovidiu and Popovici, Nicolae 2014. Local maximum points of explicitly quasiconvex functions. Optimization Letters. https://doi.org/10.1007/s11590-014-0781-3A horadam-based pseudo-random number generator
Bagdasar, O.D., Chen, M. and Bagdasar, O. 2014. A horadam-based pseudo-random number generator. IEEE. https://doi.org/10.1109/uksim.2014.55On the structure of periodic complex Horadam orbits
Bagdasar, Ovidiu D., Larcombe, Peter J., Anjum, Ashiq and Bagdasar, O. 2016. On the structure of periodic complex Horadam orbits. Carpathian Journal of Mathematics.Characterizations of Generalized Exponential Trichotomies for Linear Discrete-time Systems
Popa, I.-L., Ceauşu, T., Bagdasar, O. and Agarwal, R.P. 2016. Characterizations of Generalized Exponential Trichotomies for Linear Discrete-time Systems. Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica. 27 (2), pp. 153-166. https://doi.org/10.2478/auom-2019-0025On some functions involving the lcm and gcd of integer tuples
Bagdasar, Ovidiu 2014. On some functions involving the lcm and gcd of integer tuples. Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics. https://doi.org/10.5937/SPSUNP1402091B