Lower bounds of heights of points on hypersurfaces

Frits Beukers; Don Zagier

Acta Arithmetica (1997)

  • Volume: 79, Issue: 2, page 103-111
  • ISSN: 0065-1036

How to cite


Frits Beukers, and Don Zagier. "Lower bounds of heights of points on hypersurfaces." Acta Arithmetica 79.2 (1997): 103-111. <http://eudml.org/doc/206970>.

author = {Frits Beukers, Don Zagier},
journal = {Acta Arithmetica},
keywords = {Lower bounds of heights of points on hypersurfaces},
language = {eng},
number = {2},
pages = {103-111},
title = {Lower bounds of heights of points on hypersurfaces},
url = {http://eudml.org/doc/206970},
volume = {79},
year = {1997},

AU - Frits Beukers
AU - Don Zagier
TI - Lower bounds of heights of points on hypersurfaces
JO - Acta Arithmetica
PY - 1997
VL - 79
IS - 2
SP - 103
EP - 111
LA - eng
KW - Lower bounds of heights of points on hypersurfaces
UR - http://eudml.org/doc/206970
ER -


  1. [BS] F. Beukers and H. P. Schlickewei, The equation x+y=1 in finitely generated groups, Acta Arith. 78 (1996), 189-199. Zbl0880.11034
  2. [Le] D. H. Lehmer, Factorisation of certain cyclotomic functions, Ann. of Math. 34 (1933), 461-479. Zbl0007.19904
  3. [Lo] R. Louboutin, Sur la mesure de Mahler d'un nombre algébrique, C. R. Acad. Sci. Paris 296 (1983), 707-708. Zbl0557.12001
  4. [Sch1] H. P. Schlickewei, Equations ax+by=1, Ann. of Math., to appear. 
  5. [SW] H. P. Schlickewei and E. Wirsing, Lower bounds for the heights of solutions of linear equations, Invent. Math., to appear. Zbl0883.11013
  6. [Schm] W. M. Schmidt, Heights of algebraic points lying on curves or hypersurfaces, Proc. Amer. Math. Soc., to appear. Zbl0867.11046
  7. [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. Zbl0235.12003
  8. [Za] D. Zagier, Algebraic numbers close to both 0 and 1, Math. Comp. 61 (1993), 485-491. 
  9. [Zh] S. Zhang, Positive line bundles on arithmetic surfaces, Ann. of Math. 136 (1992), 569-587 Zbl0788.14017

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