Solved and unsolved problems οn polynomials

• Autorzy: Andrzej Schinzel
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1995
• Tom: 34
• Numer: 1
• Strony: 149-159

Daty

wydano

1995

Twórcy

autor

Andrzej Schinzel

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland

Bibliografia

• [1] A. Capelli, Sulla riduttibilita delle equazioni algebriche, Nota prima, Rend. Accad. Fis. Mat. Soc. Napoli (3), 3 (1897), 243-252.
• [2] D. Coppersmith and J. Davenport, Polynomials whose powers are sparse, Acta Arith. 58 (1991), 79-87.
• [3] E. Dobrowolski, On a question of Lehmer and the number of irreducible factors of a polynomial, Acta Arith. 34 (1979), 391-401.
• [4] F. Dorey and G. Whaples, Prime and composite polynomials, J. Algebra 28 (1974), 88-101.
• [5] A. Dubickas, On a conjecture of A. Schinzel and H. Zassenhaus, Acta Arith. 63 (1993), 15-20.
• [6] P. Erdős, On the number of terms of the square of a polynomial, Nieuw. Arch. Wiskunde (2) 23 (1949), 63-65.
• [7] M. Fried and R. E. MacRae, On the invariance of the chain of fields, Illinois J. Math. 13 (1969), 165-171.
• [8] K. Győry and A. Schinzel, On a conjecture of Posner and Rumsey, J. Number Theory 47 (1994), 63-78.
• [9] D. H. Lehmer, Factorization of certain cyclotomic functions, Ann. of Math. 34 (1933), 461-479.
• [10] R. Louboutin, Sur la mesure de Mahler d'un nombre algébrique, C. R. Acad. Sci. Paris, Sér. I 296 (1983), 539-542.
• [11] L. Rédei, Algebra, Erster Teil, Akademische Verlaggesellschaft, Leipzig, 1959.
• [12] A. Rényi, On the minimal number of terms in the square of a polynomial, Hungar. Acta Math. 1 (1947), 30-34 = Selected papers, vol. 1, Budapest 1976, 42-47.
• [13] J. F. Ritt, Prime and composite polynomials, Trans. Amer. Math. Soc., 23 (1922), 51-66.
• [14] A. Schinzel, Reducibility of lacunary polynomials I, Acta Arith. 16 (1969), 123-159.
• [15] A. Schinzel, Selected topics on polynomials, The University of Michigan Press, Ann Arbor, 1982.
• [16] A. Schinzel, On the number of terms of a power of a polynomial, Acta Arith. 49 (1987), 55-70.
• [17] A. Schinzel, On reducible trinomials, Dissertationes Math. 329 (1993).
• [18] A. Schinzel and H. Zassenhaus, A refinement of two theorems of Kronecker, Michigan Math. J. 12 (1965), 81-85.
• [19] C. J. Smyth, On the product of the conjugates outside the unit circle of an algebraic integer, Bull. London Math. Soc. 3 (1971), 169-175.
• [20] W. Verdenius, On the number of terms of the square and the cube of polynomials, Indag. Math. 11 (1949), 459-465.
• [21] U. Zannier, Ritt's second theorem for arbitrary characteristic, J. Reine Angew. Math. 445 (1993), 175-203.