Explicit ℓ2 Decoupling in Rn, Part I: Bounds for Constants in an Alternate Formulation

Z.K. Li established the first explicit decoupling estimate for the parabola in the range 4<p<6. Such explicit bounds are essential in number theory applications. Following the approach of J. Bourgain and C. Demeter, we derive an explicit bound for the implicit constant in an alternate form of decoupling in J. Bourgain and C. Demeter’s work. This is the first part of our three-part project to extend Z.K. Li’s result on the explicit bound for the decoupling constant to the n-dimensional case.