The unit equation and the cluster principle

• Autorzy: E. Bombieri , J. Mueller , M. Poe
• Języki publikacji: EN

Kategorie tematyczne

• 11D61: Exponential equations
• 11D57: Multiplicative and norm form equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 79
• Numer: 4
• Strony: 361-389

Daty

wydano

1997

otrzymano

1997-02-22

Twórcy

autor

E. Bombieri

• Institute for Advanced Study, Olden Lane, Princeton, New Jersey 08540, U.S.A.

autor

J. Mueller

• Department of Mathematics, Fordham University, Bronx, New York 10458, U.S.A.

autor

M. Poe

• Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138, U.S.A.

Bibliografia

• [BW] A. Baker and G. Wüstholz, Logarithmic forms and group varieties, J. Reine Angew. Math. 442 (1993), 19-62.
• [BS] F. Beukers and H. P. Schlickewei, The equation x+y=1 in finitely generated groups, Acta Arith. 78 (1996), 189-199.
• [C1] J. W. S. Cassels, On a class of exponential equations, Ark. Mat. 3 (1960), 231-233.
• [C2] J. W. S. Cassels, An Introduction to the Geometry of Numbers, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1959.
• [D] E. Dobrowolski, On a question of Lehmer and the number of irreducible factors of a polynomial, Acta Arith. 34 (1979), 391-401.
• [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.
• [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.
• [MKS] W. Magnus, A. Karrass and D. Solitar, Combinatorial Group Theory, 2nd ed., revised, Dover, New York, 1976.
• [P] M. Poe, On distribution of solutions of S-unit equations, J. Number Theory 62 (1997), 221-241.
• [R] P. Ribenboim, Catalan's Conjecture, Academic Press, Boston, 1994.
• [S] C. L. Siegel, Abschätzung von Einheiten, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. 9 (1969), 71-86.
• [V] J. D. Vaaler, A geometric inequality with applications to linear forms, Pacific J. Math. 83 (1979), 543-553.