Displaying similar documents to “The cubic congruence x 3 + a x 2 + b x + c 0 ( mod p ) and binary quadratic forms F ( x , y ) = a x 2 + b x y + c y 2 . II.”

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.

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.