Geodesic
A Riemann hypothesis analog for the Krawtchouk and discrete Chebyshev polynomials
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIII, Tome 507 (2021), pp. 173-182 
N. Gogin; M. Hirvensalo. A Riemann hypothesis analog for the Krawtchouk and discrete Chebyshev polynomials. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIII, Tome 507 (2021), pp. 173-182. http://geodesic.mathdoc.fr/item/ZNSL_2021_507_a9/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

As an analog to the Riemann hypothesis, we prove that the real parts of all complex zeros of the Krawtchouk polynomials, as well as of the discrete Chebyshev polynomials, of order $N=-1$ are equal to $-\frac{1}{2}$. For these polynomials, we also derive a functional equation analogous to that for the Riemann zeta function.

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