Displaying similar documents to “The arithmetic of certain del Pezzo surfaces and K3 surfaces”

Gross’ conjecture for extensions ramified over four points of 1

Po-Yi Huang (2006)

Journal de Théorie des Nombres de Bordeaux

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In this paper, under a mild hypothesis, we prove a conjecture of Gross for the Stickelberger element of the maximal abelian extension over the rational function field unramified outside a set of four degree-one places.

Manin’s conjecture for a singular sextic del Pezzo surface

Daniel Loughran (2010)

Journal de Théorie des Nombres de Bordeaux

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We prove Manin’s conjecture for a del Pezzo surface of degree six which has one singularity of type A 2 . Moreover, we achieve a meromorphic continuation and explicit expression of the associated height zeta function.

The circle method and pairs of quadratic forms

Henryk Iwaniec, Ritabrata Munshi (2010)

Journal de Théorie des Nombres de Bordeaux

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We give non-trivial upper bounds for the number of integral solutions, of given size, of a system of two quadratic form equations in five variables.