On some polynomials allegedly related to the abc conjecture

 Access to full text

 Full (PDF)

1. [1] Yu. F. Belotserkovskiĭ, Uniform distribution of algebraic numbers near the unit circle, Vestsi Akad. Navuk BSSR Ser. Fiz. Mat. Navuk 1988 (1), 49-52 (in Russian). Zbl0646.10040
2. [2] F. Beukers and H. P. Schlickewei, The equation x+y=1 in finitely generated groups, Acta Arith. 78 (1996), 189-199. Zbl0880.11034
3. [3] A. Borisov, On some polynomials, allegedly related to the abc conjecture, 1997, http://www.math.uiuc.edu/Algebraic-Number-Theory/. Zbl0903.11025
4. [4] P. Erdős and P. Turán, On the distribution of roots of polynomials, Ann. of Math. 51 (1950), 105-119. Zbl0036.01501
5. [5] J.-H. Evertse, K. Győry, C. L. Stewart and R. Tijdeman, S-unit equations and their applications, in: New Advances in Transcendence Theory (Durham, 1986), Cambridge Univ. Press, Cambridge, 1988, 110-174. 
6. [6] I. Kausz, A discriminant and an upper bound for ω² for hyperelliptic arithmetic surfaces, IHES, preprint, 1996. 
7. [7] D. Knuth, The Art of Computer Programming, Vol. 2, 2nd ed., 1981. Zbl0477.65002
8. [8] N. Koblitz, p-Adic Numbers, p-Adic Analysis, and Zeta-Functions, 2nd ed., Grad. Texts in Math. 58, Springer, New York, 1984. 
9. [9] K. Mahler, An application of Jensen's formula to polynomials, Mathematika 7 (1960), 98-100. Zbl0099.25003
10. [10] K. Mahler, An inequality for the discriminant of a polynomial, Michigan Math. J. 11 (1964), 257-262. Zbl0135.01702
11. [11] R. C. Mason, Diophantine Equations over Function Fields, London Math. Soc. Lecture Note Ser. 96, Cambridge Univ. Press, Cambridge, 1984. Zbl0533.10012
12. [12] J.-L. Nicolas et A. Schinzel, Localisation des zéros de polynômes intervenant en théorie du signal, in: Lecture Notes in Math. 1415, Springer, Berlin, 1990, 167-179. 
13. [13] J. Oesterlé, Nouvelles approches du 'théorème' de Fermat, Séminaire Bourbaki, Vol. 1987/88, Exp. 694, Astérisque 161-162 (1988), 165-186. 
14. [14] A. Schinzel, Reducibility of lacunary polynomials. IX, in: New Advances in Transcendence Theory (Durham, 1986), Cambridge Univ. Press, Cambridge, 1988, 313-336. 
15. [15] W. M. Schmidt, Diophantine Approximations and Diophantine Equations, Lecture Notes in Math. 1467, Springer, Berlin, 1991. 
16. [16] E. Selmer, On the irreducibility of certain trinomials, Math. Scand. 4 (1956), 287-302. Zbl0077.24602
17. [17] J. H. Silverman, The S-unit equation over function fields, Math. Proc. Cambridge Philos. Soc. 95 (1984), 3-4. Zbl0533.10013
18. [18] 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. Zbl0235.12003
19. [19] W. W. Stothers, Polynomial identities and Hauptmoduln, Quart. J. Math. Oxford Ser. (2) 32 (1981), 349-370. Zbl0466.12011

1. A. Borisov, M. Filaseta, T. Y. Lam, O. Trifonov, Classes of polynomials having only one non-cyclotomic irreducible factor