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math.NT2006★ 9 cited
Integral points on cubic hypersurfaces
T. D. Browning, D. R. Heath-Brown
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 equatio…
math.NT2006
Density of integer solutions to diagonal quadratic forms
T. D. Browning
Let Q be a non-singular diagonal quadratic form in at least four variables. We provide upper bounds for the number of integer solutions to the equation Q=0, which lie in a box with…