A Function Used to Locate the Zeros of an Exponential Sum

A detailed analysis is presented of the properties of a particular function that arises in the study of the zeros of exponential sums or exponential polynomials with real exponents and complex coefficients. This function originates in applications of the argument principle to determine when the imaginary parts of the zeros mod L form a dense set in the particular case of a three-term exponential sum, also known as an exponential polynomial.