Irreducibility criteria for reciprocal polynomials and applications
We present criteria for determining irreducibility of reciprocal polynomials over the field of rational numbers. We also obtain some combinatorial results concerning the irreducibility of reciprocal polynomials. As a consequence of our approach, we are able to deal with other problems such as factor...
Guardado en:
| Autor principal: | |
|---|---|
| Otros Autores: | |
| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
Mathematical Association of America
2017
|
| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
| LEADER | 04193caa a22004817a 4500 | ||
|---|---|---|---|
| 001 | PAPER-25519 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518205735.0 | ||
| 008 | 190410s2017 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-85020749679 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Cafure, A. | |
| 245 | 1 | 0 | |a Irreducibility criteria for reciprocal polynomials and applications |
| 260 | |b Mathematical Association of America |c 2017 | ||
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Barbeau, E.J., Polynomials (1989) Problem Books in Mathematics, , Springer-Verlag, New York | ||
| 504 | |a Beslin, S., De Angelis, V., The minimal polynomials of sin(2π/p) and cos(2π/p) (2004) Math. Mag, 77, pp. 146-149 | ||
| 504 | |a Dörge, K., Abschätzung der anzahl der reduziblen polynome (1965) Math. Ann, 160, pp. 59-63 | ||
| 504 | |a Dubickas, A., On the number of reducible polynomials of bounded naive height (2014) Manuscripta Math., 144, pp. 439-456 | ||
| 504 | |a Filaseta, M., (2013) Course Notes on The Theory of Irreducible Polynomials, , University of South Carolina | ||
| 504 | |a Filaseta, M., Meade, D., Irreducibility testing of lacunary 0, 1-polynomials (2005) J. Algorithms, 55, pp. 21-28 | ||
| 504 | |a Hsiao, H.J., On factorization of Chebyshev's polynomials of the first kind (1984) Bull. Inst. Math. Acad. Sin, 12, pp. 89-94 | ||
| 504 | |a Kuba, G., On the distribution of reducible polynomials (2009) Math. Slovaca, 59, pp. 349-356 | ||
| 504 | |a Mullen, G., Panario, D., (2013) Handbook of Finite Fields, , CRC Press, Boca Raton, FL | ||
| 504 | |a Niven, I., Irrational Numbers (1956) The Carus Mathematical Monographs, (11). , Mathematical Association of America, Washington, DC | ||
| 504 | |a Pólya, G., Szegö, G., (1998) Problems and Theorems in Analysis II, , Reprint of the 1976 Edition. English trans. by C. E. Billigheimer. Springer-Verlag, Berlin | ||
| 504 | |a Rivlin, T., (1974) The Chebyshev Polynomials, , John Wiley & Sons, New York | ||
| 504 | |a Rayes, M., Trevisan, V., Wang, P., Factorization properties of Chebyshev polynomials (2005) Comput. Math. Appl., 50, pp. 1231-1240 | ||
| 504 | |a Von Zur Gathen, J., Gerhard, J., (2003) Modern Computer Algebra, , Second ed. Cambridge Univ. Press, Cambridge | ||
| 504 | |a Watkins, W., Zeitlin, J., The minimal polynomial of cos(2π/n) (1993) Amer. Math. Monthly, 100, pp. 471-474 | ||
| 520 | 3 | |a We present criteria for determining irreducibility of reciprocal polynomials over the field of rational numbers. We also obtain some combinatorial results concerning the irreducibility of reciprocal polynomials. As a consequence of our approach, we are able to deal with other problems such as factorization properties of Chebyshev polynomials of the first and second kind and with the classical problems of computing minimal polynomials of algebraic values of trigonometric functions. © The Mathematical Association of America. |l eng | |
| 593 | |a Instituto del Desarrollo Humano, Universidad Nacional de General Sarmiento, J.M. Gutiérrez 1150, Los Polvorines, Buenos Aires 1613, Argentina | ||
| 593 | |a Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón III, Buenos Aires, 1428, Argentina | ||
| 593 | |a National Council of Science and Technology (CONICET), Argentina | ||
| 700 | 1 | |a Cesaratto, E. | |
| 773 | 0 | |d Mathematical Association of America, 2017 |g v. 124 |h pp. 37-53 |k n. 1 |p Am. Math. Mon. |x 00029890 |w (AR-BaUEN)CENRE-212 |t American Mathematical Monthly | |
| 856 | 4 | 1 | |u https://www.scopus.com/inward/record.uri?eid=2-s2.0-85020749679&doi=10.4169%2famer.math.monthly.124.1.37&partnerID=40&md5=0d081864238d2d74a0b5541f401cf080 |y Registro en Scopus |
| 856 | 4 | 0 | |u https://doi.org/10.4169/amer.math.monthly.124.1.37 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_00029890_v124_n1_p37_Cafure |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029890_v124_n1_p37_Cafure |y Registro en la Biblioteca Digital |
| 961 | |a paper_00029890_v124_n1_p37_Cafure |b paper |c PE | ||
| 962 | |a info:eu-repo/semantics/article |a info:ar-repo/semantics/artículo |b info:eu-repo/semantics/publishedVersion | ||
| 999 | |c 86472 | ||