EFFECTIVE l2 DECOUPLING FOR THE PARABOLA

We make effective l2Lp decoupling for the parabola in the range 4<p<6. In an appendix joint with Jean Bourgain, we apply the main theorem to prove the conjectural bound for the sixth-order correlation of the integer solutions of the equation x2+y2=m in an extremal case. This proves unconditionally a result that was proven in Bombieri and Bourgain [Int. Math. Res. Not. IMRN2015(11), 3343-3407] under the hypotheses of the Birch and Swinnerton-Dyer conjecture and the Riemann Hypothesis for L-functions of elliptic curves over Q.