Email this article Number of Nonzero Cubic Sums
- Authors: Filonov N.D.1,2
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Affiliations:
- St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences
- St. Petersburg State University
- Issue: Vol 242, No 4 (2019)
- Pages: 575-585
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/243003
- DOI: https://doi.org/10.1007/s10958-019-04497-2
- ID: 243003
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Abstract
The exponential sums \( {S}_q\left(a,m\right)=\sum \limits_{l=1}^q\exp \left(2\pi i\left({al}^3+ ml\right){q}^{-1}\right) \) are considered. For every positive integer q, closed-form expressions for the number of nonzero sums occurring among Sq(a, 0), . . . , Sq(a, q − 1) are found.
About the authors
N. D. Filonov
St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg State University
Author for correspondence.
Email: filonov@pdmi.ras.ru
Russian Federation, St. Petersburg; St. Petersburg
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