Takashi Nakamura

activity

20102026

most citedA complete Riemann zeta distribution and the Riemann hypothesis

22 citations · 53 across the 28 of their papers we have counts for

collaborators

Showing 2015Show all

5 papers · 1 filter

math.NT2015

Real zeros of Hurwitz-Lerch zeta functions in the interval $(- 1, 0)$

Takashi Nakamura

For $0 < a \leq 1$ , $s, z \in C$ and $0 < ∣ z ∣ \leq 1$ , the Hurwitz-Lerch zeta function is defined by $Φ (s, a, z) := \sum_{n = 0}^{\infty} z^{n} (n + a)^{- s}$ when $σ := ℜ (s) > 1$ . In t…

math.ST2015★ 22 cited

A complete Riemann zeta distribution and the Riemann hypothesis

Takashi Nakamura

Let $σ, t \in R$ , $s = σ + i t$ , $Γ (s)$ be the Gamma function, $ζ (s)$ be the Riemann zeta function and $ξ (s) := s (s - 1) π^{- s /2} Γ (s /2) ζ (s)$ be the complete Riemann zeta fun…

math.NT2015

Selberg's orthonormality conjecture and joint universality of L-functions

Yoonbok Lee, Takashi Nakamura, Łukasz Pańkowski

In the paper we introduce the new approach how to use an orthonormality relation of coefficients of Dirichlet series defining given L-functions from the Selberg class to prove join…

math.NT2015

Joint universality for Lerch zeta-functions

Yoonbok Lee, Takashi Nakamura, Łukasz Pańkowski

For $0 < α, λ \leq 1$ , the Lerch zeta-function is defined by $L (s; α, λ)$ $:= \sum_{n = 0}^{\infty} e^{2 π iλn} (n + α)^{- s}$ , where $σ > 1$ . In this paper, we prove joint universality for Lerch…

math.NT2015

Value distribution for the derivatives of the logarithm of $L$ -functions from the Selberg class in the half-plane of absolute convergence

Takashi Nakamura, Łukasz Pańkowski

In the present paper, we show that, for every $δ > 0$ , the function $(lo g L (s))^{(m)}$ , where $m \in N \cup {0}$ and ${\mathcal{L}} (s) := \sum_{n=1}^\infty…

Real zeros of Hurwitz-Lerch zeta functions in the interval (−1,0)

A complete Riemann zeta distribution and the Riemann hypothesis

Selberg's orthonormality conjecture and joint universality of L-functions

Joint universality for Lerch zeta-functions

Value distribution for the derivatives of the logarithm of L-functions from the Selberg class in the half-plane of absolute convergence

Real zeros of Hurwitz-Lerch zeta functions in the interval $(- 1, 0)$

Value distribution for the derivatives of the logarithm of $L$ -functions from the Selberg class in the half-plane of absolute convergence