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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


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.


Exponential Function Entire Function Real Axis Complex Variable Minus Sign 
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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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