Exponential Sums with Real Zeros 3
نویسنده
چکیده
Let Hn(z) be the function of a complex variable z defined by Hn(z) = ∑ G(±ia1 ± · · · ± ian)e iz(±b1±···±bn) where the summation is over all 2 possible plus and minus sign combinations, the same sign combination being used in both the argument of G and in the exponent. The numbers a1, a2, a3, . . . and b1, b2, b3, . . . 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 exponential sum Hn(z) has only real zeros.
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