Quadratic factors of f(x) -g(y)

Yuri F. Bilu

Acta Arithmetica (1999)

  • Volume: 90, Issue: 4, page 341-355
  • ISSN: 0065-1036

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Yuri F. Bilu. "Quadratic factors of f(x) -g(y)." Acta Arithmetica 90.4 (1999): 341-355. <http://eudml.org/doc/207332>.

@article{YuriF1999,
author = {Yuri F. Bilu},
journal = {Acta Arithmetica},
keywords = {quadratic factor; Chebyshev polynomials; Dickson polynomials; finiteness problem for Diophantine equations},
language = {eng},
number = {4},
pages = {341-355},
title = {Quadratic factors of f(x) -g(y)},
url = {http://eudml.org/doc/207332},
volume = {90},
year = {1999},
}

TY - JOUR
AU - Yuri F. Bilu
TI - Quadratic factors of f(x) -g(y)
JO - Acta Arithmetica
PY - 1999
VL - 90
IS - 4
SP - 341
EP - 355
LA - eng
KW - quadratic factor; Chebyshev polynomials; Dickson polynomials; finiteness problem for Diophantine equations
UR - http://eudml.org/doc/207332
ER -

References

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  1. [1] Yu. F. Bilu and R. F. Tichy, The Diophantine equation f(x) = g(y), submitted. Zbl0958.11049
  2. [2] P. Cassou-Noguès et J.-M. Couveignes, Factorisations explicites de g(y)- h(z), Acta Arith. 87 (1999), 291-317. Zbl0923.12004
  3. [3] W. Feit, On symmetric balanced incomplete block designs with doubly transitive automorphism groups, J. Combin. Theory Ser. A 14 (1973), 221-247. Zbl0278.05016
  4. [4] W. Feit, Some consequences of the classification of finite simple groups, in: Proc. Sympos. Pure Math. 37, Amer. Math. Soc., 1980, 175-181. Zbl0454.20014
  5. [5] M. Fried, On a conjecture of Schur, Michigan Math. J. 17 (1970), 41-55. 
  6. [6] M. Fried, The field of definition of function fields and a problem in the reducibility of polynomials in two variables, Illinois J. Math. 17 (1973), 128-146. Zbl0266.14013
  7. [7] M. Fried, On a theorem of Ritt and related Diophantine problems, J. Reine Angew. Math. 264 (1974), 40-55. Zbl0278.12101
  8. [8] M. Fried, Exposition on an arithmetic-group theoretic connection via Riemann's existence theorem, in: Proc. Sympos. Pure Math. 37, Amer. Math. Soc., 1980, 571-601. 
  9. [9] M. Fried, Variables separated polynomials, the genus 0 problem and moduli spaces, in: Number Theory in Progress (Zakopane, 1997), de Gruyter, 1999, 169-228. Zbl1053.14509
  10. [10] S. Lang, Fundamentals of Diophantine Geometry, Springer, 1983. Zbl0528.14013
  11. [11] R. Lidl, G. L. Mullen and G. Turnwald, Dickson Polynomials, Pitman Monographs Surveys Pure Math. 65, Longman Sci. Tech., 1993. 
  12. [12] J. F. Ritt, Prime and composite polynomials, Trans. Amer. Math. Soc. 23 (1922), 51-66. Zbl48.0079.01
  13. [13] D. J. S. Robinson, A Course in the Theory of Groups, Grad. Texts in Math. 80, Springer, 1982. 
  14. [14] A. Schinzel, Selected Topics on Polynomials, The Univ. of Michigan Press, Ann Arbor, MI, 1983. 
  15. [15] C. L. Siegel, Über einige Anwendungen Diophantischer Approximationen, Abh. Preuss. Akad. Wiss. Phys.-Math. Kl. 1929, Nr. 1. Zbl56.0180.05
  16. [16] G. Turnwald, On Schur's conjecture, J. Austral. Math. Soc. 58 (1995), 312-357. Zbl0834.11052
  17. [17] G. Turnwald, Some notes on monodromy groups of polynomials, in: Number Theory in Progress (Zakopane, 1997), de Gruyter, 1999, 539-552. Zbl0942.11046
  18. [18] H. A. Tverberg, A study in irreducibility of polynomials, Ph.D. thesis, Department of Mathematics, University of Bergen, 1968. Zbl0155.50001

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