Zeros of polynomials and exponential diophantine equations

B. Brindza

Compositio Mathematica (1987)

  • Volume: 61, Issue: 2, page 137-157
  • ISSN: 0010-437X

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Brindza, B.. "Zeros of polynomials and exponential diophantine equations." Compositio Mathematica 61.2 (1987): 137-157. <http://eudml.org/doc/89818>.

@article{Brindza1987,
author = {Brindza, B.},
journal = {Compositio Mathematica},
keywords = {higher degree diophantine equation; zeros of polynomials},
language = {eng},
number = {2},
pages = {137-157},
publisher = {Martinus Nijhoff Publishers},
title = {Zeros of polynomials and exponential diophantine equations},
url = {http://eudml.org/doc/89818},
volume = {61},
year = {1987},
}

TY - JOUR
AU - Brindza, B.
TI - Zeros of polynomials and exponential diophantine equations
JO - Compositio Mathematica
PY - 1987
PB - Martinus Nijhoff Publishers
VL - 61
IS - 2
SP - 137
EP - 157
LA - eng
KW - higher degree diophantine equation; zeros of polynomials
UR - http://eudml.org/doc/89818
ER -

References

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  2. Brindza, B.: On a diophantine equation connected with the Fermat equation. Acta Arith.44 (1984a) 357-363. Zbl0512.10010MR777012
  3. Brindza, B.: On S-integral solutions of the equation f(x) = ym. Acta Math. Hung.44 (1984b) 133-139. Zbl0552.10009MR759041
  4. Brindza, B., Györy, K. and Tijdeman, R.: The Fermat equation with polynomial values as base variables. Invent. Math.80 (1985) 139-151. Zbl0543.10018MR784533
  5. Brownawell, W.D. and Masser, D.W.: Vanishing sums in function fields. to appear in Math. Proc. Camb. Phil. Soc. Zbl0612.10010
  6. Everett, C.J.: Fermat's conjecture, Roth's theorem, Pythagorean triangles and Pell's equation. Duke Math. J.40 (1973) 801-804. Zbl0273.10013MR325530
  7. Györy, K.: Résultats effectifs sur la représentation des entiers par des formes décomposables. Queen's Papers in Pure and Applied Mathematics No. 56. Kingston, Canada (1980). Zbl0455.10011MR627743
  8. Györy, K.: On the number of solutions of linear equations in units of an algebraic number field. Comment. Math. Helv.54 (1979) 583-600. Zbl0437.12004MR552678
  9. Inkeri, K.: Untersuchungen über die Fermatsche Vermutung. A nn. A cad. Sc. Fenn. Ser. AI No.33 (1946) 1-60. Zbl0061.06706MR23846
  10. Inkeri, K.: A note on Fermat's conjecture. Acta Arith.39 (1976) 251-256. Zbl0287.10014MR401639
  11. Inkeri, K. and van der Poorten, A.J.: Some remarks on Fermat's conjecture. Acta Arith.39 (1976) 251-256. Zbl0287.10014
  12. Mason, R.C.: Diophantine equations over function fields. LMS Lecture Notes, No. 96. Cambridge University Press (1984). Zbl0533.10012MR754559
  13. Schinzel, A. and Tijdeman, R.: On the equation P(x) = yz. Acta Arith.31 (1976) 199-204. Zbl0339.10018MR422150
  14. Schinzel, A. and Zassenhaus, H.: A refinement of two theorems of Kronecker. Michigan Math. J.12 (1965) 81-85. Zbl0128.03402MR175882
  15. Shorey, T.N. and Stewart, C.L.: On the diophantine equation ax2t + bxty + y2 = d and pure powers in recurrence sequences. Math. Scand.52 (1983) 24-26. Zbl0491.10016MR697495
  16. Shorey, T.N. and Tijdeman, R.: Exponential diophantine equations. Cambridge University Press, New York, in press. Zbl0606.10011MR891406
  17. Sprindžuk, V.G.: Classical diophantine equations in two unknowns (Russian). Nauka, Moskva (1982). Zbl0523.10008MR685430
  18. Stark, H.M.: Effective estimates of solutions of some diophantine equations. Acta Arith.24 (1973) 251-259. Zbl0272.10010MR340175
  19. Stewart, C.L.: A note on the Fermat equation. Mathematika24 (1977) 130-132. Zbl0348.10011MR469865
  20. Tijdeman, R.: Applications of the Gel'fond-Baker method to rational number theory. Topics in Number Theory, Proc. Conf. Debrecen1974, Colloq. Math. Soc. János Bolyai13. North Holland, Amsterdam (1976) 399-416. Zbl0335.10022MR560494
  21. Turk, J.: On the difference between perfect powers. Acta Arith., to appear. Zbl0587.10010MR847290
  22. Zimmert, R.: Ideale kleiner Norm in Idealklassen und eine Regulatorabschätzung. Invent. Math.62 (1981) 367-380. Zbl0456.12003MR604833

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