Geodesic
On stationary phase integrals
Glasgow mathematical journal, Tome 36 (1994) no. 3, pp. 355-362

Voir la notice de l'article provenant de la source Cambridge University Press

Let f(x) and g(x) be real functions defined on the interval [a, b], with f(x) at least twice continuously differentiable, f′(x) monotone increasing, and f(x) of bounded variation. We consider the exponential integralwhere e(t) denotes exp 2πit. The purpose of this note is to prove sharp forms of the well-known estimates:A: If f′(x) is nonzero on [a, b], then I has order of magnitudeThe constant of proportionality depends on the function g(x).B: If f′(x) changes sign at x = c with a < c < b, then 
Huxley, M. N. On stationary phase integrals. Glasgow mathematical journal, Tome 36 (1994) no. 3, pp. 355-362. doi: 10.1017/S0017089500030962
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