Journal of the Ramanujan Mathematical Society

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On the Smallest Point on a Diagonal Quartic Threefold


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1 Mathematisches Institut der Universitat Gottingen, Bunsenstraße 3–5, D-37073 Gottingen, Germany
     

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For the family a0x4 = a1y4 + a2z4 + a3v4 + a4w4, a0, . . . , a4 > 0, of diagonal quartic threefolds, we study the behaviour of the height of the smallest rational point versus the Tamagawa type number introduced by E. Peyre.
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  • On the Smallest Point on a Diagonal Quartic Threefold

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Authors

Andreas-Stephan Elsenhans
Mathematisches Institut der Universitat Gottingen, Bunsenstraße 3–5, D-37073 Gottingen, Germany
Jorg Jahnel
Mathematisches Institut der Universitat Gottingen, Bunsenstraße 3–5, D-37073 Gottingen, Germany

Abstract


For the family a0x4 = a1y4 + a2z4 + a3v4 + a4w4, a0, . . . , a4 > 0, of diagonal quartic threefolds, we study the behaviour of the height of the smallest rational point versus the Tamagawa type number introduced by E. Peyre.