Integral points on cubic hypersurfaces

T.D. Browning, R. Heath Brown, in:, Analytic Number Theory: Essays in Honour of Klaus Roth, Cambridge University Press, 2009, pp. 75–90.

Book Chapter | Published
Author
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Abstract
Let g be a cubic polynomial with integer coefficients and n>9 variables, and assume that the congruence g=0 modulo p^k is soluble for all prime powers p^k. We show that the equation g=0 has infinitely many integer solutions when the cubic part of g defines a projective hypersurface with singular locus of dimension <n-10. The proof is based on the Hardy-Littlewood circle method.
Publishing Year
Date Published
2009-01-31
Book Title
Analytic Number Theory: Essays in honour of Klaus Roth
Page
75 - 90
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Cite this

Browning TD, Heath Brown R. Integral points on cubic hypersurfaces. In: Analytic Number Theory: Essays in Honour of Klaus Roth. Cambridge University Press; 2009:75-90.
Browning, T. D., & Heath Brown, R. (2009). Integral points on cubic hypersurfaces. In Analytic Number Theory: Essays in honour of Klaus Roth (pp. 75–90). Cambridge University Press.
Browning, Timothy D, and Roger Heath Brown. “Integral Points on Cubic Hypersurfaces.” In Analytic Number Theory: Essays in Honour of Klaus Roth, 75–90. Cambridge University Press, 2009.
T. D. Browning and R. Heath Brown, “Integral points on cubic hypersurfaces,” in Analytic Number Theory: Essays in honour of Klaus Roth, Cambridge University Press, 2009, pp. 75–90.
Browning TD, Heath Brown R. 2009. Integral points on cubic hypersurfaces. Analytic Number Theory: Essays in honour of Klaus Roth. 75–90.
Browning, Timothy D., and Roger Heath Brown. “Integral Points on Cubic Hypersurfaces.” Analytic Number Theory: Essays in Honour of Klaus Roth, Cambridge University Press, 2009, pp. 75–90.

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