Northcott's theorem on heights I. A general estimate |
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| Authors: | Wolfgang M. Schmidt |
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| Affiliation: | (1) Department of Mathematics, University of Colorado, 80309 Boulder, CO, USA |
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| Abstract: | Given a pointP=(ao:...:an) of projective space  n=n (A) whereA is the field of algebraic numbers, letd(P) be its degree andH(P) its absolute multiplicative height. Northcott's Theorem says that givend, n andX, there are only finitely many pointsP n withd(P) d andH(P)X. We will show that there are at mostc(d, n)Xd(d+n) such points.Supported in part by NSF grant DMS-9108581. |
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