# The circle method and pairs of quadratic forms

```@article{Iwaniec2010TheCM,
title={The circle method and pairs of quadratic forms},
author={Henryk Iwaniec and Ritabrata Munshi},
journal={Journal de Theorie des Nombres de Bordeaux},
year={2010},
volume={22},
pages={403-419}
}```
• Published 2010
• Mathematics
• 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

### Rational points on singular intersections of quadrics

• Mathematics
Compositio Mathematica
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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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