Integral points on quadrics with prime coordinates |
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Authors: | Jianya Liu |
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Institution: | 1.School of Mathematics,Shandong University,Jinan,China;2.School of Mathematics,Institute for Advanced Study,Princeton,USA |
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Abstract: | Let f (x 1, . . . , x s ) be a regular indefinite integral quadratic form, and t an integer. Denote by V the affine quadric {x : f (x) = t}, and by \({V(\mathbb {P})}\) the set of \({{\bf x}\in V}\) whose coordinates are simultaneously prime. It is proved that, under suitable conditions, \({V(\mathbb{P})}\) is Zariski dense in V as long as s ≥ 10. |
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