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2000 | 95 | 3 | 261-288
Tytuł artykułu

The Diophantine equation f(x) = g(y)

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Czasopismo
Rocznik
Tom
95
Numer
3
Strony
261-288
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-12-17
Twórcy
autor
  • Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051 Basel, Switzerland
  • Institut für Mathematik (A), Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria
Bibliografia
  • [1] R. M. Avanzi and U. Zannier, Genus one curves defined by separated variable polynomials, Acta Arith., to appear.
  • [2] A. Baker, Bounds for solutions of superelliptic equations, Proc. Cambridge Philos. Soc. 65 (1969), 439-444.
  • [3] F. Beukers, T. N. Shorey and R. Tijdeman, Irreducibility of polynomials and arithmetic progressions with equal product of terms, in: [21], pp. 11-26.
  • [4] Yu. Bilu, Integral points and Galois covers, Mat. Contemp. 14 (1998), 1-11.
  • [5] Yu. Bilu, Quadratic factors of f(x)-g(y), Acta Arith. 90 (1999), 341-355.
  • [6] Yu. F. Bilu, B. Brindza, Á. Pintér and R. F. Tichy, On some diophantine problems related to power sums and binomial coefficients, in preparation.
  • [7] Yu. Bilu and G. Hanrot, Solving superelliptic Diophantine equations by Baker's method, Compositio Math. 112 (1998), 273-312.
  • [8] Yu. F. Bilu, T. Stoll and R. F. Tichy, Diophantine equations for the Meixner polynomials, in preparation.
  • [9] B. Brindza and Á. Pintér, On the irreducibility of some polynomials in two variables, Acta Arith. 82 (1997), 303-307.
  • [10] Y. Bugeaud, Bounds for the solutions of superelliptic equations, Compositio Math. 107 (1997), 187-219.
  • [11] P. Cassou-Noguès et J.-M. Couveignes, Factorisations explicites de g(y)-h(z), Acta Arith. 87 (1999), 291-317.
  • [12] H. Davenport, D. J. Lewis and A. Schinzel, Equations of the form f(x) = g(y), Quart. J. Math. Oxford Ser. (2) 12 (1961), 304-312.
  • [13] J.-H. Evertse and J. H. Silverman, Uniform bounds for the number of solutions to $Y^n=f(X)$, Math. Proc. Cambridge Philos. Soc. 100 (1986), 237-248.
  • [14] W. Feit, On symmetric balanced incomplete block designs with doubly transitive automorphism groups, J. Combin. Theory Ser. A 14 (1973), 221-247.
  • [15] W. Feit, Some consequences of the classification of finite simple groups, in: Proc. Sympos. Pure Math. 37, Amer. Math. Soc., 1980, 175-181.
  • [16] 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.
  • [17] M. Fried, Arithmetical properties of function fields (II). The generalized Schur problem, Acta Arith. 25 (1973/74), 225-258.
  • [18] M. Fried, On a theorem of Ritt and related Diophantine problems, J. Reine Angew. Math. 264 (1974), 40-55.
  • [19] 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.
  • [20] M. Fried, Variables separated polynomials, the genus 0 problem, and moduli spaces, in: [21], pp. 169-228.
  • [21] K. Győry, H. Iwaniec and J. Urbanowicz (eds.), Number Theory in Progress (Proc. Internat. Conf. in Number Theory in Honor of A. Schinzel, Zakopane, 1997), de Gruyter, 1999.
  • [22] P. Kirschenhofer, A. Pethő and R. F. Tichy, On analytical and Diophantine properties of a family of counting polynomials, Acta Sci. Math. (Szeged) 65 (1999), 47-59.
  • [23] S. Lang, Fundamentals of Diophantine Geometry, Springer, 1983.
  • [24] W. J. LeVeque, On the equation $y^m=f(x)$, Acta Arith. 9 (1964), 209-219.
  • [25] R. Lidl, G. L. Mullen and G. Turnwald, Dickson Polynomials, Pitman Monographs Surveys Pure Appl. Math. 65, Longman Sci. Tech., 1993.
  • [26] J. F. Ritt, Prime and composite polynomials, Trans. Amer. Math. Soc. 23 (1922), 51-66.
  • [27] A. Schinzel, Selected Topics on Polynomials, The Univ. of Michigan Press, Ann Arbor, 1982.
  • [28] J.-P. Serre, Lectures on the Mordell-Weil Theorem, Aspects Math. E15, Vieweg, Braunschweig, 1989.
  • [29] C. L. Siegel, The integer solutions of the equation $y^2= ax^n + bx^n-1 +...+ k$, J. London Math. Soc. 1 (1926), 66-68; also: Gesammelte Abhandlungen, Band 1, 207-208.
  • [30] C. L. Siegel, Über einige Anwendungen Diophantischer Approximationen, Abh. Preuss. Akad. Wiss. Phys.-Math. Kl., 1929, Nr. 1; also: Gesammelte Abhandlungen, Band 1, 209-266.
  • [31] V. G. Sprindžuk, Classical Diophantine Equations in Two Unknowns, Nauka, Moscow, 1982 (in Russian); English transl.: Lecture Notes in Math. 1559, Springer, 1994.
  • [32] G. Turnwald, On Schur's conjecture, J. Austral. Math. Soc. 58 (1995), 312-357.
  • [33] H. A. Tverberg, A study in irreducibility of polynomials, Ph.D. thesis, Dept. of Math., Univ. of Bergen, 1968.
  • [34] P. M. Voutier, On the number of S-integral solutions to $Y^m=f(X)$, Monatsh. Math. 119 (1995), 125-139.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav95z3p261bwm
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