Research in Number Theory

, 5:27 | Cite as

Counting rational points on Kummer surfaces

  • Andreas MalmendierEmail author
  • Yih Sung


We consider the problem of counting the number of rational points on the family of Kummer surfaces associated with two non-isogenous elliptic curves. For this two-parameter family we prove Manin’s unity, using the presentation of the Kummer surfaces as isotrivial elliptic fibration and as double cover of the modular elliptic surface of level two. By carrying out the rational point-count with respect to either of the two elliptic fibrations explicitly, we obtain an interesting new identity between two-parameter counting functions.


Kummer surface Manin principle Rational points 

Mathematics Subject Classification

14D0x 14J28 33C65 



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Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUtah State UniversityLoganUSA

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