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Title
This thesis presents various results concerning the density of rational and integral points on algebraic varieties. These results are proven with methods from analytic number theory as well as algebraic geometry. Using exponential sums in several var...
We give upper bounds for the number of integral solutions of bounded height to a system of equations $f_i(x_1,\ldots,x_n) = 0$, $1 \leq i \leq r$, where the $f_i$ are polynomials with integer coefficients. The estimates are obtained by generalising a...
We prove an upper bound for the number of representations of a positive integer N as the sum of four kth powers of integers of size at most B, using a new version of the determinant method developed by Heath-Brown, along with recent results by Salber...
This thesis presents various results concerning the density of rational and integral points on algebraic varieties. These results are proven with methods from analytic number theory as well as algebraic geometry. Using exponential sums in several var...
We study the hexagonal lattice $\mathbb{Z}[\omega]$, where $\omega^6=1$. More specifically, we study the angular distribution of hexagonal lattice points on circles with a fixed radius. We prove that the angles are equidistributed on average, and sug...