10 april 2008, kl 14.15, Uppsala, Ångström sal 80115

Per Salberger (Chalmers): Counting solutions to Diophantine equations

Abstract. We present some new results on the asymptotic behaviour of the number of integral solutions of Diophantine equations in boxes. To obtain such results one applies usually the Hardy-Littlewood circle method. But this does not work well for polynomials of high degree in few variables. One can then use the determinant method of Bombieri-Pila and Heath-Brown instead.