Martinez, Cesar and Sombra, Martin (2019) An arithmetic Berntein-Kunirenko inequality. MATHEMATISCHE ZEITSCHRIFT, 291 (3-4). pp. 1211-1244. ISSN 0025-5874, 1432-1823
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We present an upper bound for the height of the isolated zeros in the torus of a system of Laurent polynomials over an adelic field satisfying the product formula. This upper bound is expressed in terms of the mixed integrals of the local roof functions associated to the chosen height function and to the system of Laurent polynomials. We also show that this bound is close to optimal in some families of examples. This result is an arithmetic analogue of the classical Berntein-Kunirenko theorem. Its proof is based on arithmetic intersection theory on toric varieties.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; Height of points; Laurent polynomials; Mixed integrals; Toric varieties; u-Resultants |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Walter Gubler |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 15 Apr 2020 12:04 |
| Last Modified: | 15 Apr 2020 12:04 |
| URI: | https://pred.uni-regensburg.de/id/eprint/27255 |
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