Abstract
This paper proves such a new Hilbert’s Nullstellensatz for analytic trigonometric polynomials that if {fj}j=1n≥2 are analytic trigonometric polynomials without common zero in the finite complex plane ℂ then there are analytic trigonometric polynomials {gj}j=1n≥2 obeying ∑j=1n≥2fjgj=1 in ℂ, thereby not only strengthening Helmer’s Principal Ideal Theorem for entire functions, but also finding an intrinsic path from Hilbert’s Nullstellensatz for analytic polynomials to Pythagoras’ Identity on ℂ.
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