Geodesic
Asymptotics and formulas for cubic exponential sums
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic number theory, Tome 299 (2017), pp. 86-104

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Several asymptotic expansions and formulas for cubic exponential sums are derived. The expansions are most useful when the cubic coefficient is in a restricted range. This generalizes previous results in the quadratic case and helps to clarify how to numerically approximate cubic exponential sums and how to obtain upper bounds for them in some cases.
Keywords: cubic exponential sums, van der Corput iteration. 
@article{TM_2017_299_a4,
     author = {Ghaith A. Hiary},
     title = {Asymptotics and formulas for cubic exponential sums},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {86--104},
     publisher = {mathdoc},
     volume = {299},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2017_299_a4/}
}
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Ghaith A. Hiary. Asymptotics and formulas for cubic exponential sums. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic number theory, Tome 299 (2017), pp. 86-104. http://geodesic.mathdoc.fr/item/TM_2017_299_a4/