arXiv subjects

Keita Nakai

Publications and source records attributed to Keita Nakai.

6 recordsLinked to original sources

arXiv2026

On the value distribution of the Riemann zeta-function with general shifts

This paper studies the value distribution of the Riemann zeta-function under general shifts. We establish discrepancy estimates for the Bohr--Jessen limit theorem for a broad class of shifts. We also prove a universality theorem for logarithmic-power shifts, which are not covered by previous universality results for general shifts. Furthermore, we obtain a quantitative Bohr--Jessen limit theorem for logarithmic-power shifts.

math.NT↗

arXiv2025

Effective hybrid joint universality for Dirichlet $L$-functions and its application

In 2003, Garunkštis provided a lower bound for the lower density of the universality theorem for the Riemann zeta-function. In this paper, we generalize this result for the hybrid joint universality theorem for Dirichlet $L$-functions whose moduli are prime numbers. Furthermore, by its application, we estimate a lower bound of the lower density of the universality theorem for Hurwitz zeta-functions with rational parameters.

math.NT↗

arXiv2024

Joint Universality for the Riemann zeta-function with general shifts

Laurinčikas proposed that whether the universality theorem for the Riemann zeta-function shifted by an exponential function holds or not. This problem is solved for more general shifts by Andersson et al. In this paper, we generalize their result for the joint universality theorem for the Riemann zeta-function with general shifts using a different approach from their method.

math.NT↗

arXiv2024

Discrete universality for Matsumoto zeta-functions and the nontrivial zeros of the Riemann zeta-function

In 2017, Garunkštis, Laurinčikas and Macaitienė proved the discrete universality theorem for the Riemann zeta-function sifted by the nontrivial zeros of the Riemann zeta-function. This discrete universality has been extended in various zeta-functions and $L$-functions. In this paper, we generalize this discrete universality for Matsumoto zeta-functions.

math.NT↗

arXiv2023

Notes on Universality in Short Intervals and Exponential Shifts

We improve a recent universality theorem for the Riemann zeta-function in short intervals due to Antanas Laurinčikas with respect to the length of these intervals. Moreover, we prove that the shifts can even have exponential growth. This research was initiated by two questions proposed by Laurin\v cikas in a problem session of a recent workshop on universality.

math.NT↗

arXiv2023

Universality for the iterated integrals of logarithms of $L$-functions in the Selberg class

We prove the universality theorem for the iterated integrals of logarithms of $L$-functions in the Selberg class on some line parallel to the real axis.

math.NT↗