Displaying similar documents to “On the representation of numbers by the direct sums of some binary quadratic forms.”

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.

CM liftings of supersingular elliptic curves

Ben Kane (2009)

Journal de Théorie des Nombres de Bordeaux

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Assuming GRH, we present an algorithm which inputs a prime p and outputs the set of fundamental discriminants D < 0 such that the reduction map modulo a prime above p from elliptic curves with CM by 𝒪 D to supersingular elliptic curves in characteristic p is surjective. In the algorithm we first determine an explicit constant D p so that | D | > D p implies that the map is necessarily surjective and then we compute explicitly the cases | D | < D p .