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, Tome 22 (2010) no. 2, pp. 403-419.

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

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.

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, Tome 22 (2010) no. 2, pp. 403-419. doi : 10.5802/jtnb.724. https://www.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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