# Journal of the Ramanujan Mathematical Society

Volume 34, Issue 3, September 2019 pp. 271–279.

Sufficient conditions for the existence of rational points on diagonal cubic surfaces

**Authors**:
Yosuke Shimizu

**Author institution:**Bannnai laboratory at Keio University in Japan

**Summary: **
In this paper, we construct diagonal cubic surfaces over
Q which have a Q-rational point under the
assumption that the Tate-Shafarevich group of elliptic curve
X3 + Y3=AZ3 is finite. We can also check that there is no
Brauer-Manin obstruction for these surfaces without the finiteness
assumption of the Tate-Shafarevich
group.

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