A Riemann Hypothesis Analog for the Krawtchouk and Discrete Chebyshev Polynomials - UTU Research Portal

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A Riemann Hypothesis Analog for the Krawtchouk and Discrete Chebyshev Polynomials

Authors: Gogin Nikita, Hirvensalo Mika

Publisher: Springer

Publication year: 2022

Journal: Journal of Mathematical Sciences

Journal name in source: Journal of Mathematical Sciences (United States)

Volume: 261

First page : 709

Last page: 716

DOI: https://doi.org/10.1007/s10958-022-05782-3

Web address : https://link.springer.com/article/10.1007/s10958-022-05782-3#author-information

Abstract

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 −1/2. For these polynomials, we also derive a functional equation analogous to that for the Riemann zeta function.