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

Voir la notice de l'article 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. 
@article{ZNSL_2021_507_a9,
     author = {N. Gogin and M. Hirvensalo},
     title = {A {Riemann} hypothesis analog for the {Krawtchouk} and discrete {Chebyshev} polynomials},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {173--182},
     publisher = {mathdoc},
     volume = {507},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_507_a9/}
}
TY  - JOUR
AU  - N. Gogin
AU  - M. Hirvensalo
TI  - A Riemann hypothesis analog for the Krawtchouk and discrete Chebyshev polynomials
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2021
SP  - 173
EP  - 182
VL  - 507
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2021_507_a9/
LA  - en
ID  - ZNSL_2021_507_a9
ER  - 
%0 Journal Article
%A N. Gogin
%A M. Hirvensalo
%T A Riemann hypothesis analog for the Krawtchouk and discrete Chebyshev polynomials
%J Zapiski Nauchnykh Seminarov POMI
%D 2021
%P 173-182
%V 507
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2021_507_a9/
%G en
%F ZNSL_2021_507_a9
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/