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Proceedings of the American Mathematical Society

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Zero-free regions of exponential sums

Author: Kenneth B. Stolarsky
Journal: Proc. Amer. Math. Soc. 83 (1981), 486-488
MSC: Primary 32A10; Secondary 30C15
MathSciNet review: 627675
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Abstract: If the sum of the exponentials of the components of a complex $ n$-vector $ P = ({z_1}, \ldots ,{z_n})$ vanishes, then $ P$ is at least $ [1 + o(1)]$ln $ n$ from the diagonal of complex $ n$-space, and this is essentially best possible.

References [Enhancements On Off] (What's this?)

  • [1] G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, Cambridge, 1964.
  • [2] M. Lakshmanamurti, On the upper bound of ∑ⁿᵢ₌₁𝑥ᵢ^{𝑚} subject to the conditions ∑𝑥ᵢ=0 and ∑𝑥ᵢ²=𝑛, Math. Student 18 (1950), 111–116. MR 0044589

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Keywords: Complex $ n$-space, exponential sums, power sums, zero-free regions
Article copyright: © Copyright 1981 American Mathematical Society