On the Density of Integer Points on Generalised Markoff-hurwitz Hypersurfaces
نویسندگان
چکیده
We use bounds of mixed character sums modulo a square-free integer q of a special structure to estimate the density of integer points on the hypersurface f1(x1) + . . . + fn(xn) = ax k1 1 . . . x kn n for some polynomials fi ∈ Z[X] and nonzero integers a and ki, i = 1, . . . , n. In the case of f1(X) = . . . = fn(X) = X 2 and k1 = . . . = kn = 1 the above hypersurface is known as the Markoff-Hurwitz hypersurface. Our results are substantially stronger than those known for general hypersurfaces.
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