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On the gaps between zeros of trigonometric polynomials

Gady Kozma·Ferenc Oravecz
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Abstract

We show that for every finite symetric set S of integer vectors, every real trigonometric polynomial on the d dimensional torus with spectrum in S has a zero in every closed ball of diameter D, where D is the sum over S of 1 over 4 times the L2 norm of the vector. We investigate tightness in some special cases.

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Gady Kozma, Ferenc Oravecz. 2006-01-02. On the gaps between zeros of trigonometric polynomials. https://arxiv.org/abs/math/0601021

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