논문KCI 등재
On the irreducibility of sum of two reciprocal polynomials
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For a certain kind of reciprocal polynomials $P(x), Q(x)\in \mathbb{Z}[x]$, their sums are considered. We demonstrate that the Mahler measure of polynomials plays a role to prove the irreducibility of the sums over the field of rationals.
Abstract
For a certain kind of reciprocal polynomials $P(x), Q(x)\in \mathbb{Z}[x]$, their sums are considered. We demonstrate that the Mahler measure of polynomials plays a role to prove the irreducibility of the sums over the field of rationals.
참고문헌 (10)
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- H. Kleiman, "On irreducibility criteria of Dickson", J. London Math. Soc. (2), 7, pp.467~475 (1974)
- L. Kronecker, "Zwei Satze uber Gleichungen mit ganzzahligen Coefficienten", J. Reine Angew. Math, 53, pp.173~175 (1857)
- D. Y. Kwon, "Minimal polynomials of some beta-numbers and Chebyshev polynomials", Acta Arith, 130(4), pp.321~332 (2007)
- D. Y. Kwon, "Reciprocal polynomials with all zeros on the unit circle", Acta Math. Hungar, 131(3), pp.285~294 (2011)
- P. Lakatos, "On zeros of reciprocal polynomials", Publ. Math. Debrecen, 61(3-4), pp.645~661 (2002)
- D. H. Lehmer, "Factorization of certain cyclotomic functions", Ann. of Math. (2), 34(3), pp.461~479 (1933)
- C. L. Siegel, "Algebraic integers whose conjugates lie in the unit circle", Duke Math. J, 11, pp.597~602 (1944)
- C. J. Smyth, "On the product of the conjugates outside the unit circle of an algebraic integer", Bull. London Math. Soc, 3, pp.169~175 (1971)
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