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Zeros of random trigonometric polynomials

For a certain nonconvex optimization problem, I need to know the expected number of real zeros of trigonometric polynomials.

\[0=\sum_{k=1}^{k=N}A(k)\sin(kx)A(k)\cos(kx)\]

This is not exactly the usual sense of polynomial.

This is well studied for i.i.d. standard normal coefficients \(A(k),b(k)\). I need more general results; in particular I need to relax the identical distribution assumption. I wonder if this is a case where a worst-case result might be easier than a stochastic one?

Reading: [@FlascheExpected2017;@GarciaBrief2002;@VanderbeiComplex2015;@DumitrescuPositive2017;@EdelmanHow1995].

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