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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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 507, 2021, pp. 173–182.
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Gogin, N., Hirvensalo, M. A Riemann Hypothesis Analog for the Krawtchouk and Discrete Chebyshev Polynomials. J Math Sci 261, 709–716 (2022). https://doi.org/10.1007/s10958-022-05782-3
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DOI: https://doi.org/10.1007/s10958-022-05782-3