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The large degree asymptotics of the expected number of real zeros of a randomtrigonometric polynomial $$ T_n(x) = \sum_ {j=0} ^{n} a_j \cos (j x) + b_j \sin(j x), \ x \in (0,2\pi), $$ with i.i.d. real-valued standard Gaussiancoefficients is known to be $ 2n / \sqrt{3} $. In this article, we considerquite a different and extreme setting on the set of the coefficients of $ T_n$. We show that a random trigonometric polynomial of degree $ n $ with $ \ell$-periodic i.i.d. Gaussian coefficients is expected to have significantly morereal zeros compared to the classical case with i.i.d. Gaussian coefficients.More precisely, the expected number of real zeros of $ T_n $ is proportional to$ n $ with a proportionality constant $ \mathrm{C}_{\ell,r} \in (\sqrt{2},2] $,which is explicitly represented by a double integral formula. The case $ r=0 $is marked as a special one since in such a case $ T_n $ asymptotically obtainsthe largest possible number of real zeros

Real zeros of random trigonometric polynomials with $ \ell $-periodic coefficients