The construction of resonance curves in the author's monograph ‘Area, Lattice Points, and Exponential Sums’ is modified so that the resonance curves now have a differential equation, a functorial mapping property, and better approximation properties.
"Resonance curves in the Bombieri-Iwaniec method." Funct. Approx. Comment. Math. 32 7 - 49, 2004. https://doi.org/10.7169/facm/1538186623