The density of integral points on hypersurfaces of degree at least four

Details The density of integral points on hypersurfaces of degree at least four The density of integral points on hypersurfaces of degree at least four

2008-08-21

arxiv.org/abs/0808.2910v2

Acta Arith. 141 (2010), 211-240.

Mathematics

Number Theory

31 pages. Thoroughly revised due to errors in the first version. Main result slightly weakened

Scientific paper

Let $f$ be a polynomial of degree at least four with integer-valued
coefficients. We establish new bounds for the density of integer solutions to
the equation $f=0$, using an iterated version of Heath-Browns $q$-analogue of
van der Corput's method of exponential sums.

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