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JOURNALS // Chebyshevskii Sbornik // Archive

Chebyshevskii Sb., 2021 Volume 22, Issue 5, Pages 359–364 (Mi cheb1141)

This article is cited in 1 paper

BRIEF MESSAGE

About one functional equation

M. N. Dobrovol'skiia, N. N. Dobrovol'skiibc, N. M. Dobrovol'skiib

a Geophysical centre of RAS (Moscow)
b Tula State Lev Tolstoy Pedagogical University (Tula)
c Tula State University (Tula)

Abstract: The hyperbolic zeta function of a two-dimensional lattice of Dirichlet approximations is studied. A functional equation is found for the hyperbolic zeta function of a two-dimensional lattice of Dirichlet approximations in the case of rational $\beta$, which sets an analytical continuation on the entire complex plane, except for the point $\alpha=1$, in which the pole is of the first order.
The found functional equation allows us to raise the question of continuity for the hyperbolic zeta function of a two-dimensional lattice of Dirichlet approximations in the case of rational $\beta$.

Keywords: Riemann zeta function, Dirichlet series, Hurwitz zeta function.

UDC: 511.3

Received: 19.06.2021
Accepted: 21.12.2021

DOI: 10.22405/2226-8383-2021-22-5-359-364



© Steklov Math. Inst. of RAS, 2025