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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Volume 299, Pages 86–104
DOI: https://doi.org/10.1134/S0371968517040057 (Mi tm3850) 		 
Asymptotics and formulas for cubic exponential sums

Ghaith A. Hiary

Department of Mathematics, The Ohio State University, 231 West 18th Ave., Columbus, OH 43210, USA
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DOI: https://doi.org/10.1134/S0371968517040057
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.
Keywords: cubic exponential sums, van der Corput iteration.
Funding agency Grant number
National Science Foundation DMS-1406190
The research is supported in part by the National Science Foundation under agreement no. DMS-1406190.
Received: July 11, 2017
English version:
Proceedings of the Steklov Institute of Mathematics, 2017, Volume 299, Pages 78–95
DOI: https://doi.org/10.1134/S0081543817080053
Bibliographic databases:
Document Type: Article
UDC: 511.33
MSC: Primary 11L03, 11L15; Secondary 11Y35
Language: Russian
Citation: Ghaith A. Hiary, “Asymptotics and formulas for cubic exponential sums”, Analytic number theory, On the occasion of the 80th anniversary of the birth of Anatolii Alekseevich Karatsuba, Trudy Mat. Inst. Steklova, 299, MAIK Nauka/Interperiodica, Moscow, 2017, 86–104; Proc. Steklov Inst. Math., 299 (2017), 78–95
Citation in format AMSBIB
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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