no. 2
The circle method and pairs of quadratic forms
Iwaniec, Henryk1; Munshi, Ritabrata2
1 Rutgers University 110, Frelinghuysen Road Piscataway NJ 08854, USA
2 School of Mathematics Tata Institute of Fundamental Research Homi Bhabha Road Mumbai 400005, India
Journal de théorie des nombres de Bordeaux, Volume 22 (2010) no. 2, pp. 403-419.

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.

Nous donnons une majoration non triviale du nombre de solutions entières, de taille donnée, d’un système de deux formes quadratiques en cinq variables.

DOI: 10.5802/jtnb.724
Classification: 11D45, 11P55
Iwaniec, Henryk 1; Munshi, Ritabrata 2

1 Rutgers University 110, Frelinghuysen Road Piscataway NJ 08854, USA
2 School of Mathematics Tata Institute of Fundamental Research Homi Bhabha Road Mumbai 400005, India 
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Iwaniec, Henryk; Munshi, Ritabrata. The circle method and pairs of quadratic forms. Journal de théorie des nombres de Bordeaux, Volume 22 (2010) no. 2, pp. 403-419. doi : 10.5802/jtnb.724. http://archive.numdam.org/articles/10.5802/jtnb.724/

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[2] T.D. Browning, An overview of Manin’s conjecture for del Pezzo surfaces. Analytic Number Theory - A Tribute to Gauss and Dirichlet (Goettingen, 20th June - 24th June, 2005), Clay Mathematics Proceedings 7 (2007), 39–56. | Zbl

[3] W. Duke; J.B. Friedlander; H. Iwaniec, Bounds for automorphic L-functions. Invent. Math. 112 (1993), no. 1, 1–8. | Zbl

[4] D.R. Heath-Brown, A new form of the circle method, and its application to quadratic forms. J. Reine Angew. Math. 481 (1996), 149–206. | Zbl

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