Counting Integral Points on Universal Torsors
نویسندگان
چکیده
منابع مشابه
1 3 Fe b 20 09 COUNTING INTEGRAL POINTS ON UNIVERSAL TORSORS
— Manin’s conjecture for the asymptotic behavior of the number of rational points of bounded height on del Pezzo surfaces can be approached through universal torsors. We prove several auxiliary results for the estimation of the number of integral points in certain regions on universal torsors. As an application, we prove Manin’s conjecture for a singular quartic del Pezzo surface.
متن کاملO ct 2 00 8 COUNTING INTEGRAL POINTS ON UNIVERSAL TORSORS
— Manin’s conjecture for the asymptotic behavior of the number of rational points of bounded height on del Pezzo surfaces can be approached through universal torsors. We prove several auxiliary results for the estimation of the number of integral points in certain regions on universal torsors. As an application, we prove Manin’s conjecture for a singular quartic del Pezzo surface.
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Given a lattice polytope P (with underlying lattice L), the universal counting function UP (L ) = |P ∩ L| is defined on all lattices L containing L. Motivated by questions concerning lattice polytopes and the Ehrhart polynomial, we study the equation UP = UQ. Mathematics Subject Classification: 52B20, 52A27, 11P21 Partially supported by Hungarian Science Foundation Grant T 016391, and by the Fr...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2009
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnp030