The Asymptotics of Points of Bounded Height on Diagonal Cubic and Quartic Threefolds

  • Andreas-Stephan Elsenhans
  • Jörg Jahnel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4076)


For the families ax 3 = by 3 + z 3 + v 3 + w 3, a, b = 1, ... ,100, and ax 4 = by 4 + z 4 + v 4 + w 4, a, b = 1, ... ,100, of projective algebraic threefolds, we test numerically the conjecture of Manin (in the refined form due to Peyre) about the asymptotics of points of bounded height on Fano varieties.


Rational Point Complete Intersection Diophantine Equation Rational Line Fano Variety 
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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Andreas-Stephan Elsenhans
    • 1
  • Jörg Jahnel
    • 1
  1. 1.Mathematisches InstitutUniversität GöttingenGöttingenGermany

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