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Kenta Endo

Publications and source records attributed to Kenta Endo.

7 recordsLinked to original sources
arXiv2024

Limit theorem for the hybrid joint universality theorem on zeta and $L$-functions

In 1979, Gonek presented the hybrid joint universality theorem for Dirichlet $L$-functions and proved the universality theorem for Hurwitz zeta-functions with rational parameter as an application. Following the introduction of the hybrid universality theorem, several generalizations, refinements, and applications have been developed. Despite these advancements, no probabilistic proof based on Bagchi's approach has been formulated due to the complexities of adapting his method to the hybrid joint universality theorem. In this paper, we prove the limit theorem for the hybrid joint universality theorem.

math.NT↗
arXiv2021

Effective uniform approximation by $L$-functions in the Selberg class

Recently, Garunkštis, Laurinčikas, Matsumoto, J. & R. Steuding showed an effective universality-type theorem for the Riemann zeta-function by using an effective multi-dimensional denseness result of Voronin. We will generalize Voronin's effective result and their theorem to the elements of the Selberg class satisfying some conditions.

math.NT↗
arXiv2020

On the value-distribution of iterated integrals of the logarithm of the Riemann zeta-function I: denseness

We consider iterated integrals of $\logζ(s)$ on certain vertical and horizontal lines. Here, the function $ζ(s)$ is the Riemann zeta-function. It is a well known open problem whether or not the values of the Riemann zeta-function on the critical line are dense in the complex plane. In this paper, we give a result for the denseness of the values of the iterated integrals on the horizontal lines. By using this result, we obtain the denseness of the values of $\int_{0}^{t} \log ζ(1/2 + it')dt'$ under the Riemann Hypothesis. Moreover, we show that, for any $m\geq 2$, the denseness of the values of an $m$-times iterated integral on the critical line is equivalent to the Riemann Hypothesis.

math.NT↗
arXiv2020

Hypergroups and distance distributions of random walks on graphs

Wildberger's construction enables us to obtain a hypergroup from a special graph via random walks. We will give a probability theoretic interpretation to products on the hypergroup. The hypergroup can be identified with a commutative algebra whose basis is transition matrices. We will estimate the operator norm of such a transition matrix and clarify a relationship between their matrix products and random walks.

math.PR↗
arXiv2017

Real zeros of Hurwitz zeta-functions and their asymptotic behavior in the interval $(0,1)$

Let $0<a\leq1, s\in\mathbb{C}$, and $ζ(s,a)$ be the Hurwitz zeta-function. Recently, T.~Nakamura showed that $ζ(σ,a)$ does not vanish for any $0<σ<1$ if and only if $1/2\leq a \leq1$. In this paper, we show that $ζ(σ,a)$ has precisely one zero in the interval $(0,1)$ if $0<a<1/2$. Moreover, we reveal the asymptotic behavior of this unique zero with respect to $a$.

math.NT↗