@article{bwmeta1.element.bwnjournal-article-aav84i2p109bwm, author = {Alexandr Borisov}, title = {On some polynomials allegedly related to the abc conjecture}, journal = {Acta Arithmetica}, volume = {84}, year = {1998}, pages = {109-128}, zbl = {0903.11025}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav84i2p109bwm} }
Alexandr Borisov. On some polynomials allegedly related to the abc conjecture. Acta Arithmetica, Tome 84 (1998) pp. 109-128. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav84i2p109bwm/
[000] [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). | Zbl 0646.10040
[001] [2] F. Beukers and H. P. Schlickewei, The equation x+y=1 in finitely generated groups, Acta Arith. 78 (1996), 189-199. | Zbl 0880.11034
[002] [3] A. Borisov, On some polynomials, allegedly related to the abc conjecture, 1997, http://www.math.uiuc.edu/Algebraic-Number-Theory/. | Zbl 0903.11025
[003] [4] P. Erdős and P. Turán, On the distribution of roots of polynomials, Ann. of Math. 51 (1950), 105-119. | Zbl 0036.01501
[004] [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.
[005] [6] I. Kausz, A discriminant and an upper bound for ω² for hyperelliptic arithmetic surfaces, IHES, preprint, 1996.
[006] [7] D. Knuth, The Art of Computer Programming, Vol. 2, 2nd ed., 1981. | Zbl 0477.65002
[007] [8] N. Koblitz, p-Adic Numbers, p-Adic Analysis, and Zeta-Functions, 2nd ed., Grad. Texts in Math. 58, Springer, New York, 1984.
[008] [9] K. Mahler, An application of Jensen's formula to polynomials, Mathematika 7 (1960), 98-100. | Zbl 0099.25003
[009] [10] K. Mahler, An inequality for the discriminant of a polynomial, Michigan Math. J. 11 (1964), 257-262. | Zbl 0135.01702
[010] [11] R. C. Mason, Diophantine Equations over Function Fields, London Math. Soc. Lecture Note Ser. 96, Cambridge Univ. Press, Cambridge, 1984. | Zbl 0533.10012
[011] [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.
[012] [13] J. Oesterlé, Nouvelles approches du 'théorème' de Fermat, Séminaire Bourbaki, Vol. 1987/88, Exp. 694, Astérisque 161-162 (1988), 165-186.
[013] [14] A. Schinzel, Reducibility of lacunary polynomials. IX, in: New Advances in Transcendence Theory (Durham, 1986), Cambridge Univ. Press, Cambridge, 1988, 313-336.
[014] [15] W. M. Schmidt, Diophantine Approximations and Diophantine Equations, Lecture Notes in Math. 1467, Springer, Berlin, 1991.
[015] [16] E. Selmer, On the irreducibility of certain trinomials, Math. Scand. 4 (1956), 287-302. | Zbl 0077.24602
[016] [17] J. H. Silverman, The S-unit equation over function fields, Math. Proc. Cambridge Philos. Soc. 95 (1984), 3-4. | Zbl 0533.10013
[017] [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. | Zbl 0235.12003
[018] [19] W. W. Stothers, Polynomial identities and Hauptmoduln, Quart. J. Math. Oxford Ser. (2) 32 (1981), 349-370. | Zbl 0466.12011