Counting rational points on Kummer surfaces
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Publication:2320012
DOI10.1007/S40993-019-0166-XzbMATH Open1442.14040arXiv1901.11151OpenAlexW3100236789MaRDI QIDQ2320012
Author name not available (Why is that?)
Publication date: 21 August 2019
Published in: (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/1901.11151
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