Abstract
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.
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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Vol. 299, pp. 86–104.
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Hiary, G.A. Asymptotics and Formulas for Cubic Exponential Sums. Proc. Steklov Inst. Math. 299, 78–95 (2017). https://doi.org/10.1134/S0081543817080053
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DOI: https://doi.org/10.1134/S0081543817080053