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, Volume 113, Issue 3, pp 307–317 | Cite as

Sums of exponential functions having only real zeros

  • David A. CardonEmail author
Article

Abstract.

Let H n (z) be the function of a complex variable z defined by where the summation is over all 2 n possible plus and minus sign combinations, the same sign combination being used in both the argument of G and in the exponent. The numbers \({{a_1,a_2,a_3,\ldots}}\) and \({{b_1,b_2,b_3,\ldots}}\) are assumed to be positive, and G is an entire function of genus 0 or 1 that is real on the real axis and has only real zeros. Then the function H n (z) has only real zeros.

Keywords

Exponential Function Entire Function Real Axis Complex Variable Minus Sign 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsBrigham Young UniversityUT ProvoUSA

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