Zero-free regions of exponential sums
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- by Kenneth B. Stolarsky PDF
- Proc. Amer. Math. Soc. 83 (1981), 486-488 Request permission
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
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G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, Cambridge, 1964.
- M. Lakshmanamurti, On the upper bound of $\sum ^n_{i=1}x_i^m$ subject to the conditions $\sum x_i=0$ and $\sum x_i^2=n$, Math. Student 18 (1950), 111–116. MR 44589
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 486-488
- MSC: Primary 32A10; Secondary 30C15
- DOI: https://doi.org/10.1090/S0002-9939-1981-0627675-4
- MathSciNet review: 627675