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

• Autorzy: Yuri F. Bilu
• Języki publikacji: EN

Kategorie tematyczne

• 12E05: Polynomials (irreducibility, etc.)
• 12E10: Special polynomials

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 90
• Numer: 4
• Strony: 341-355

Daty

wydano

1999

otrzymano

1998-08-28

poprawiono

1999-03-12

Twórcy

autor

Yuri F. Bilu

• Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051 Basel, Switzerland

Bibliografia

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