ArticleOriginal scientific text

Title

On some polynomials allegedly related to the abc conjecture

Authors 1

Affiliations

  1. Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802, U.S.A.

Bibliography

  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).
  2. F. Beukers and H. P. Schlickewei, The equation x+y=1 in finitely generated groups, Acta Arith. 78 (1996), 189-199.
  3. A. Borisov, On some polynomials, allegedly related to the abc conjecture, 1997, http://www.math.uiuc.edu/Algebraic-Number-Theory/.
  4. P. Erdős and P. Turán, On the distribution of roots of polynomials, Ann. of Math. 51 (1950), 105-119.
  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. I. Kausz, A discriminant and an upper bound for ω² for hyperelliptic arithmetic surfaces, IHES, preprint, 1996.
  7. D. Knuth, The Art of Computer Programming, Vol. 2, 2nd ed., 1981.
  8. N. Koblitz, p-Adic Numbers, p-Adic Analysis, and Zeta-Functions, 2nd ed., Grad. Texts in Math. 58, Springer, New York, 1984.
  9. K. Mahler, An application of Jensen's formula to polynomials, Mathematika 7 (1960), 98-100.
  10. K. Mahler, An inequality for the discriminant of a polynomial, Michigan Math. J. 11 (1964), 257-262.
  11. R. C. Mason, Diophantine Equations over Function Fields, London Math. Soc. Lecture Note Ser. 96, Cambridge Univ. Press, Cambridge, 1984.
  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. J. Oesterlé, Nouvelles approches du 'théorème' de Fermat, Séminaire Bourbaki, Vol. 1987/88, Exp. 694, Astérisque 161-162 (1988), 165-186.
  14. A. Schinzel, Reducibility of lacunary polynomials. IX, in: New Advances in Transcendence Theory (Durham, 1986), Cambridge Univ. Press, Cambridge, 1988, 313-336.
  15. W. M. Schmidt, Diophantine Approximations and Diophantine Equations, Lecture Notes in Math. 1467, Springer, Berlin, 1991.
  16. E. Selmer, On the irreducibility of certain trinomials, Math. Scand. 4 (1956), 287-302.
  17. J. H. Silverman, The S-unit equation over function fields, Math. Proc. Cambridge Philos. Soc. 95 (1984), 3-4.
  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.
  19. W. W. Stothers, Polynomial identities and Hauptmoduln, Quart. J. Math. Oxford Ser. (2) 32 (1981), 349-370.
Pages:
109-128
Main language of publication
English
Received
1996-12-02
Accepted
1997-10-30
Published
1998
Exact and natural sciences