Translator Disclaimer
2010 On the Smallest Point on a Diagonal Cubic Surface
Andreas-Stephan Elsenhans, Jörg Jahnel
Experiment. Math. 19(2): 181-193 (2010).

Abstract

For diagonal cubic surfaces $S$, we study the behavior of the height $\m(S)$ of the smallest rational point versus the Tamagawa-type number $\tau(S)$ introduced by E. Peyre. We determined both quantities for a sample of $849{,}781$ diagonal cubic surfaces. Our methods are explained in some detail. The results suggest an inequality of the type $\smash{\m(S) < C(\varepsilon)/\tau(S)^{1+\varepsilon}}$. We conclude the article with the construction of a sequence of diagonal cubic surfaces showing that the inequality $\m(S) < C/\tau(S)$ is false in general.

Citation

Download Citation

Andreas-Stephan Elsenhans. Jörg Jahnel. "On the Smallest Point on a Diagonal Cubic Surface." Experiment. Math. 19 (2) 181 - 193, 2010.

Information

Published: 2010
First available in Project Euclid: 17 June 2010

zbMATH: 1233.11072
MathSciNet: MR2676747

Subjects:
Primary: 11G35, 11G40, 11G50

Rights: Copyright © 2010 A K Peters, Ltd.

JOURNAL ARTICLE
13 PAGES


SHARE
Vol.19 • No. 2 • 2010
Back to Top