On Fully Split Lacunary Polynomials in Finite Fields

• Autorzy: Bibak K. , Shparlinski I. E.

Identyfikatory

DOI

10.4064/ba59-3-1

• Języki publikacji: EN

Abstrakty

EN

We estimate the number of possible degree patterns of k-lacunary polynomials of degree t< p which split completely modulo p. The result is based on a combination of a bound on the number of zeros of lacunary polynomials with some graph theory arguments.

Słowa kluczowe

EN

roots of lacunary polynomials; finite fields; domination number

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2011
• Tom: Vol. 59, no 3
• Strony: 197--202
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Bibak K.

• Department of Combinatorics and Optimization University of Waterloo Waterloo, Ontario, Canada N2L 3G1

autor

Shparlinski I. E.

• Department of Computing Macquarie University Sydney, NSW 2109, Australia

Bibliografia

• [1] R. Canetti, J. B. Friedlander, S. V. Konyagin, M. Larsen, D. Lieman and I. E. Shparlinski, On the statistical properties of Diffie-Hellman distributions, Israel J. Math. 120 (2000), 23-46.
• [2] Q. Cheng, S. Tarasov and M. Vyalyi, Efficient algorithms for sparse cyclotomic integer zero testing, Theory Comput. Syst. 46 (2010), 120-142.
• [3] W. E. Clark, B. Shekhtman, S. Suen and D. C. Fisher, Upper bounds for the domination number of a graph, Congr. Numer. 132 (1998), 99-123.
• [4] M. Filaseta, A. Granville and A. Schinzel, Irreducibility and greatest common divisor algorithms for sparse polynomials, in: Number Theory and Polynomials, London Math. Soc. Lecture Note Ser. 352, Cambridge Univ. Press, 2008, 155-176.
• [5] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Oxford Univ. Press, Oxford, 1979.
• [6] T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Domination in Graphs, Dekker, 1998.
• [7] H. W. Lenstra, Finding small degree factors of lacunary polynomials, in: Number Theory in Progress (Zakopane, 1997), Vol. 1, de Gruyter, Berlin, 1999, 267-276.
• [8] |, On the factorization of lacunary polynomials, in: Number Theory in Progress (Zakopane, 1997), Vol. 1, de Gruyter, Berlin, 1999, 277-291.
• [9] O. Ore, Theory of Graphs, Amer. Math. Soc. Colloq. Publ. 38, 1962.
• [10] A. Schinzel, Reducibility of lacunary polynomials, XII, Acta Arith. 90 (1999), 273-289.