Abstract : The delta symbol developed by Duke-Friedlander-Iwaniec and Heath-Brown has played an important role in studying rational points on hypersurfaces of low degrees. We present a two dimensional delta symbol and apply it to establish a quantitative Hasse principle for a smooth intersection of two quadratic forms defined over $Q$ in at least ten variables. The goal of these delta symbols is to carry out a (double) Kloosterman refinement of the circle method. This is based on a joint work with Simon Rydin Myerson and Pankaj Vishe.

Keywords : circle method; delta symbol; diophantine equations; Kloosterman refinement; quadratic forms; Hasse principle; Manin-Peyre conjecture