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On ternary quadratic forms that represent zero

Published online by Cambridge University Press:  18 May 2009

C. Hooley
Affiliation:
School of MathematicsUniversity of Wales College of CardiffCardiff
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Serre [6] has recently created a theory of some generality in response to a query from Manin about the size of the number N(x) of (indefinite) ternary quadratic forms AX2 + BY2 + CZ2 that represent zero and have coefficients of magnitudes not exceeding x.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1993

References

REFERENCES

1.Burgess, D. A., On character sums and L-series. II, Proc. London Math. Soc. (3) 13 (1963), 524536.Google Scholar
2.Halberstam, H. and Richert, H. E., Sieve methods (Academic Press, 1974).Google Scholar
3.Hooley, C., On the intervals between numbers that are sums of two squares. III, J. Reine Angew. Math. 267 (1974), 207218.Google Scholar
4.Hooley, C., Applications of sieve methods to the theory of numbers (Cambridge University Press, 1976).Google Scholar
5.Legendre, A.-M., Théorie des Nombres, 3rd ed. (Firmin-Didot, 1830), I, 3339.Google Scholar
6.Serre, J.-P., Spécialisation des éléments de Br2(Q(T1,…, T2)), C.R. Acad. Sci. Paris Sér. I Math. 311 (1990), 397402.Google Scholar