Number of Nonzero Cubic Sums


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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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