Some applications of Baker's sharpened bounds to diophantine equations

Robert Tijdeman

Séminaire Delange-Pisot-Poitou. Théorie des nombres (1974-1975)

  • Volume: 16, Issue: 2, page 1-7

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Tijdeman, Robert. "Some applications of Baker's sharpened bounds to diophantine equations." Séminaire Delange-Pisot-Poitou. Théorie des nombres 16.2 (1974-1975): 1-7. <http://eudml.org/doc/110902>.

@article{Tijdeman1974-1975,
author = {Tijdeman, Robert},
journal = {Séminaire Delange-Pisot-Poitou. Théorie des nombres},
language = {eng},
number = {2},
pages = {1-7},
publisher = {Secrétariat mathématique},
title = {Some applications of Baker's sharpened bounds to diophantine equations},
url = {http://eudml.org/doc/110902},
volume = {16},
year = {1974-1975},
}

TY - JOUR
AU - Tijdeman, Robert
TI - Some applications of Baker's sharpened bounds to diophantine equations
JO - Séminaire Delange-Pisot-Poitou. Théorie des nombres
PY - 1974-1975
PB - Secrétariat mathématique
VL - 16
IS - 2
SP - 1
EP - 7
LA - eng
UR - http://eudml.org/doc/110902
ER -

References

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  1. [1] Baker ( A.). - Linear forms in the logarithms of algebraic numbers, I, II, III, IV, Mathematika, London, t. 13, 1966, p. 204-216 ; t. 14, 1967, p. 102-107, 220-228 ; t. 15, 1968, p. 204-216. Zbl0161.05201MR258756
  2. [2] Baker ( A.). - Contributions to the theory of diophantine equations, I : On the representation of integers by binary forms, Phil. Trans. Roy. Soc. London, Series A, t. 263, 1968, p. 173-191. Zbl0157.09702MR228424
  3. [3] Baker ( A.). - Bounds for the solutions of the hyperelliptic equation, Proc. Camb. phil. Soc., t. 65, 1969, p. 439-444. Zbl0174.33803MR234912
  4. [4] Baker ( A.). - A sharpening of the bounds for linear forms in logarithms, I, II, III, Acta Arith., Warszawa, t. 21, 1972, p. 117-129 ; t. 24, 1973, p. 33-36 ; t. 27, 1975, p. 247-252. Zbl0244.10031
  5. [5] Coates ( J. ). - An effective p-adic analogue of a theorem of Thue, II : The greatest prime factor of a binary form, Acta Arith., Warszawa, t. 16, 1970, p. 399-412. Zbl0221.10026MR263741
  6. [6] Čudnovskij ( G.V.). - Some analytic methods in the theory of diophantine approximations [in Russian], Preprint 74-9, Math. Institute Acad. Sc. Ukrainian S.S.R., Kiev, 1974. 
  7. [7] Hyyrö ( S.). - Über die Gleichung axn - byn = z und das Catalansche Problem, Ann. Acad. Sc. Fenn. , Ser. A, 1964, n° 355. Zbl0137.25705MR205925
  8. [8] Kotov ( S.V.). - Greatest prime factor of a polynomial, Math. Notes, t. 13, 1973, p. 313-317 ; [in Russian], Mat. Zametki, t. 13, 1973, p. 515-522. Zbl0267.12002MR327670
  9. [9] Lebesgue ( V.A.). - Sur l'impossibilité en nombres entiers de l'équation xm = y2 + 1 , Nouv. Ann. Math., t. 9, 1850, p. 178-181. 
  10. [10] Roth ( K.F.). - Rational approximations to algebraic numbers, Mathematika, London, t. 2, 1955, p. 1-20 ; Corrigendum, ibid., p. 168. Zbl0064.28501MR72182
  11. [11] Schinzel ( A.) and Tijdeman ( R.). - On the equation ym = P(x) , Acta Arith., Warszawa (to appear). Zbl0339.10018MR422150
  12. [12] Schmidt ( W.M.). - Simultaneous approximation to algebraic numbers by rationals, Acta Math., Uppsala, t. 125, 1970, p. 189-201. Zbl0205.06702MR268129
  13. [13] Shorey ( T.N.) and Tijdeman ( R.). - On the greatest prime factor of a polynomial at integer points (to appear). Zbl0338.10040
  14. [14] Siegel ( C.L.). - The integer solutions of the equation y2 = axn+bxn-1+...+k , J. London math. Soc., t. 1, 1926, p. 66-68 (under the pseudonym X.). 
  15. [15] Siegel ( C.L.). - Über einige Anwendungen diophantischer Approximationen, Abh. Preuss. Akad. Wiss., 1929, n° 1, 70 p. Zbl56.0180.05JFM56.0180.05
  16. [16] Siegel ( C.L.). - Die Gleichung axn - byn = c , Math. Annalen, t. 114, 1937, p. 57-68. Zbl0015.38902MR1513124
  17. [17] Sprindžuk ( V.G.). - Representation of numbers by the norm forms with two dominating variables, J. Number Theory, t. 6, 1974, p. 481-486. Zbl0304.10012MR354567
  18. [18] Thue ( A.). - Über Annäherungswerte algebraïscher Zahlen, J. für reine angew. Math., t. 135, 1909. p. 284-305. JFM40.0265.01
  19. [19] Tijdeman ( R.). - On the equation of Catalan, Acta Arith., Warszawa (to appear). Zbl0286.10013MR404137

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