Email this article Asymptotics of sums with Gaussian kernel and multiplicative coefficients
- Authors: Zinchenko A.S.1, Romanenkov A.M.1
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Affiliations:
- Moscow Aviation Institute (National Research University)
- Issue: Vol 29, No 2 (2025)
- Pages: 381-389
- Section: Short Communications
- URL: https://journal-vniispk.ru/1991-8615/article/view/349677
- DOI: https://doi.org/10.14498/vsgtu2113
- EDN: https://elibrary.ru/BCHVZM
- ID: 349677
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Abstract
This study deals with the asymptotic behavior of finite sums containing a Gaussian function and a multiplicative term. Such sums naturally arise in complexity analysis of binary tree traversal and ray searching algorithms. Using the method of complex integration, we transform the discrete finite sum into an integral along an infinite vertical line in the complex plane. We demonstrate that the integrand contains a positive integer power of the Riemann zeta function. By applying standard residue calculation techniques, we obtain the asymptotic value of this integral.
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##article.viewOnOriginalSite##About the authors
Alexandr S. Zinchenko
Moscow Aviation Institute (National Research University)
Email: zinchenkoas@mai.ru
ORCID iD: 0000-0001-7971-4572
SPIN-code: 7948-5040
Scopus Author ID: 59124941500
ResearcherId: AAJ-2633-2020
https://www.mathnet.ru/rus/person229294
Cand. Econom. Sci.; Associate Professor; Dept. of Mathematics
Russian Federation, 125993, Moscow, Volokolamskoe Shosse, 4Alexander M. Romanenkov
Moscow Aviation Institute (National Research University)
Author for correspondence.
Email: romanaleks@gmail.com
ORCID iD: 0000-0002-0700-8465
SPIN-code: 7586-0934
Scopus Author ID: 57196480014
ResearcherId: AAH-9530-2020
https://www.mathnet.ru/rus/person29785
Cand. Techn. Sci., Associate Professor; Associate Professor; Dept. of Mathematics
Russian Federation, 125993, Moscow, Volokolamskoe Shosse, 4References
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