The unit equation and the cluster principle

E. Bombieri; J. Mueller; M. Poe

Acta Arithmetica (1997)

  • Volume: 79, Issue: 4, page 361-389
  • ISSN: 0065-1036

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E. Bombieri, J. Mueller, and M. Poe. "The unit equation and the cluster principle." Acta Arithmetica 79.4 (1997): 361-389. <http://eudml.org/doc/206984>.

@article{E1997,
author = {E. Bombieri, J. Mueller, M. Poe},
journal = {Acta Arithmetica},
keywords = {unit equation; cluster principle},
language = {eng},
number = {4},
pages = {361-389},
title = {The unit equation and the cluster principle},
url = {http://eudml.org/doc/206984},
volume = {79},
year = {1997},
}

TY - JOUR
AU - E. Bombieri
AU - J. Mueller
AU - M. Poe
TI - The unit equation and the cluster principle
JO - Acta Arithmetica
PY - 1997
VL - 79
IS - 4
SP - 361
EP - 389
LA - eng
KW - unit equation; cluster principle
UR - http://eudml.org/doc/206984
ER -

References

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  1. [BW] A. Baker and G. Wüstholz, Logarithmic forms and group varieties, J. Reine Angew. Math. 442 (1993), 19-62. Zbl0788.11026
  2. [BS] F. Beukers and H. P. Schlickewei, The equation x+y=1 in finitely generated groups, Acta Arith. 78 (1996), 189-199. Zbl0880.11034
  3. [C1] J. W. S. Cassels, On a class of exponential equations, Ark. Mat. 3 (1960), 231-233. 
  4. [C2] J. W. S. Cassels, An Introduction to the Geometry of Numbers, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1959. 
  5. [D] E. Dobrowolski, On a question of Lehmer and the number of irreducible factors of a polynomial, Acta Arith. 34 (1979), 391-401. Zbl0416.12001
  6. [EGST] J.-H. Evertse, K. Győry, C. L. Stewart and R. Tijdeman, On S -unit equations in two unknowns, Invent. Math. 92 (1988), 461-477. Zbl0662.10012
  7. [G] K. Győry, On the number of solutions of linear equations in units of an algebraic number field, Comment. Math. Helv. 54 (1979), 583-600. Zbl0437.12004
  8. [MKS] W. Magnus, A. Karrass and D. Solitar, Combinatorial Group Theory, 2nd ed., revised, Dover, New York, 1976. 
  9. [P] M. Poe, On distribution of solutions of S-unit equations, J. Number Theory 62 (1997), 221-241. Zbl0879.11015
  10. [R] P. Ribenboim, Catalan's Conjecture, Academic Press, Boston, 1994. Zbl0824.11010
  11. [S] C. L. Siegel, Abschätzung von Einheiten, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. 9 (1969), 71-86. Zbl0186.36703
  12. [V] J. D. Vaaler, A geometric inequality with applications to linear forms, Pacific J. Math. 83 (1979), 543-553. Zbl0465.52011

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