Displaying similar documents to “More cubic surfaces violating the Hasse principle”

The arithmetic of certain del Pezzo surfaces and K3 surfaces

Dong Quan Ngoc Nguyen (2012)

Journal de Théorie des Nombres de Bordeaux

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We construct del Pezzo surfaces of degree 4 violating the Hasse principle explained by the Brauer-Manin obstruction. Using these del Pezzo surfaces, we show that there are algebraic families of K 3 surfaces violating the Hasse principle explained by the Brauer-Manin obstruction. Various examples are given.

The geometry of the third moment of exponential sums

Florent Jouve (2008)

Journal de Théorie des Nombres de Bordeaux

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We give a geometric interpretation (and we deduce an explicit formula) for two types of exponential sums, one of which is the third moment of Kloosterman sums over F q of type K ( ν 2 ; q ) . We establish a connection between the sums considered and the number of F q -rational points on explicit smooth projective surfaces, one of which is a K 3 surface, whereas the other is a smooth cubic surface. As a consequence, we obtain, applying Grothendieck-Lefschetz theory, a generalized formula for the third moment...

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.