Resonance curves in the Bombieri-Iwaniec method (Q1769806)

The \textit{E. Bombieri} and \textit{H. Iwaniec} method [Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 13, 449--472 (1986; Zbl 0615.10047)] for estimating exponential sums, and lattice points below a curve \(y= g(x)\), gives rise to the problem of counting integer points close to certain ``resonance curves'', as described in the author's work [Area, lattice points, and exponential sums (LMS Monographs, 13) Oxford: Oxford Univ. Press (1996; Zbl 0861.11002)]. This paper gives a thorough investigation of these curves, obtaining a more precise version of the above relationship between integer points and resonance curves. Future applications to exponential sums are promised.