Lower bounds of heights of points on hypersurfaces

• Autorzy: Frits Beukers , Don Zagier
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 79
• Numer: 2
• Strony: 103-111

Daty

wydano

1997

otrzymano

1996-03-18

Twórcy

autor

Frits Beukers

• Department of Mathematics, University of Utrecht, Budapestlaan 6, P.O. Box 80010 3508 TA Utrecht, The Netherlands

autor

Don Zagier

• Max-Planck-Institut für Mathematik, Gottfried-Claren-Str. 26, 53225 Bonn, Germany

Bibliografia

• [BS] F. Beukers and H. P. Schlickewei, The equation x+y=1 in finitely generated groups, Acta Arith. 78 (1996), 189-199.
• [Le] D. H. Lehmer, Factorisation of certain cyclotomic functions, Ann. of Math. 34 (1933), 461-479.
• [Lo] R. Louboutin, Sur la mesure de Mahler d'un nombre algébrique, C. R. Acad. Sci. Paris 296 (1983), 707-708.
• [Sch1] H. P. Schlickewei, Equations ax+by=1, Ann. of Math., to appear.
• [SW] H. P. Schlickewei and E. Wirsing, Lower bounds for the heights of solutions of linear equations, Invent. Math., to appear.
• [Schm] W. M. Schmidt, Heights of algebraic points lying on curves or hypersurfaces, Proc. Amer. Math. Soc., to appear.
• [Sm] C. J. Smyth, On the product of the conjugates outside the unit circle of an algebraic integer, Bull. London Math. Soc. 3 (1971), 169-175.
• [Za] D. Zagier, Algebraic numbers close to both 0 and 1, Math. Comp. 61 (1993), 485-491.
• [Zh] S. Zhang, Positive line bundles on arithmetic surfaces, Ann. of Math. 136 (1992), 569-587