The circle method and pairs of quadratic forms

  title={The circle method and pairs of quadratic forms},
  author={Henryk Iwaniec and Ritabrata Munshi},
  journal={Journal de Theorie des Nombres de Bordeaux},
Nous donnons une majoration non triviale du nombre de solutions entieres, de taille donnee, d'un systeme de deux formes quadratiques en cinq variables. 

On pairs of quadratic forms in five variables

In this paper, we obtain an upper bound for the number of integral solutions, of given height, of system of two quadratic forms in five variables. Our bound is an improvement over the bound given in

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Abstract Given an intersection of two quadrics $X\subset { \mathbb{P} }^{m- 1} $, with $m\geq 9$, the quantitative arithmetic of the set $X( \mathbb{Q} )$ is investigated under the assumption that



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This paper surveys recent progress towards the Manin conjecture for (singular and non-singular) del Pezzo surfaces. To illustrate some of the techniques available, an upper bound of the expected

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A new form of the circle method, and its application to quadratic forms.

If the coefficients r(n) satisfy suitable arithmetic conditions the behaviour of F (α) will be determined by an appropriate rational approximation a/q to α, with small values of q usually producing

Browning , On Manin ’ s conjecture for singular del Pezzo surfaces of degree 4

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On Manin's conjecture for singular del Pezzo surfaces of degree 4. I. Michigan Math

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Ritabrata Munshi School of Mathematics Tata Institute of Fundamental Research Homi Bhabha Road Mumbai 400005