arXiv subjects

Yoshinori Mizuno

Publications and source records attributed to Yoshinori Mizuno.

4 recordsLinked to original sources

arXiv2026

Genus character $L$-functions of orders in quadratic function fields

We define genus character $L$-functions of orders in quadratic function fields of odd characteristic. We express each as a product of two quadratic $L$-functions and explicit local factors at primes dividing the conductor, with a possible shift of the variable in one of the two quadratic $L$-functions. This product formula yields meromorphic continuation and functional equations. In the real case, we evaluate special values in terms of continued fractions and derive formulas for the product of class numbers of two imaginary quadratic function fields. These formulas are function field analogues of the Kaneko-Mizuno-Zagier formula.

math.NT↗

arXiv2026

Review of LHD-ECRH activities and beyond

The electron cyclotron resonance heating (ECRH) system on the Large Helical Device (LHD) played a key role in the progress of helical fusion research from the first plasma in 1998 to the final discharge on December 25, 2025. This paper presents a historical review of ECRH activities on LHD, highlighting the stepwise advances in hardware, including gyrotrons, transmission lines, and launcher systems, together with the exploration of advanced plasma regimes such as overdense heating and long-pulse steady-state operation. Beyond plasma heating, the ECRH system was also used as a high-power probe for advanced diagnostics, including collective Thomson scattering (CTS) as well as correlation electron cyclotron emission (CECE), and as a flexible actuator for transport studies and real-time control experiments. Finally, we discuss how the technological assets and operational expertise accumulated over the nearly three decades of the LHD program are being further developed and applied to next-generation helical devices, particularly CHD and CHD-U, as well as to broader gyrotron and millimeter-wave applications.

physics.plasm-ph↗

arXiv2022

Congruences on the class numbers of $\mathbb{Q}(\sqrt{\pm 2p})$ for $p\equiv3$ $(\text{mod }4)$ a prime

For a prime $p\equiv 3$ $(\text{mod }4)$, let $h(-8p)$ and $h(8p)$ be the class numbers of $\mathbb{Q}(\sqrt{-2p})$ and $\mathbb{Q}(\sqrt{2p})$, respectively. Let $Ψ(ξ)$ be the Hirzebruch sum of a quadratic irrational $ξ$. We show that $h(-8p)\equiv h(8p)\Big(Ψ(2\sqrt{2p})/3-Ψ\big((1+\sqrt{2p})/2\big)/3\Big)$ $(\text{mod }16)$. Also, we show that $h(-8p)\equiv 2h(8p)Ψ(2\sqrt{2p})/3$ $(\text{mod }8)$ if $p\equiv 3$ $(\text{mod }8)$, and $h(-8p)\equiv \big(2h(8p)Ψ(2\sqrt{2p})/3\big)+4$ $(\text{mod }8)$ if $p\equiv 7$ $(\text{mod }8)$.

math.NT↗

arXiv2022

Congruences for odd class numbers of quadratic fields with odd discriminant

For any distinct two primes $p_1\equiv p_2\equiv 3$ $(\text{mod }4)$, let $h(-p_1)$, $h(-p_2)$ and $h(p_1p_2)$ be the class numbers of the quadratic fields $\mathbb{Q}(\sqrt{-p_1})$, $\mathbb{Q}(\sqrt{-p_2})$ and $\mathbb{Q}(\sqrt{p_1p_2})$, respectively. Let $ω_{p_1p_2}:=(1+\sqrt{p_1p_2})/2$ and let $Ψ(ω_{p_1p_2})$ be the Hirzebruch sum of $ω_{p_1p_2}$. We show that $h(-p_1)h(-p_2)\equiv h(p_1p_2)Ψ(ω_{p_1p_2})/n$ $(\text{mod }8)$, where $n=6$ (respectively, $n=2$) if $\min\{p_1,p_2\}>3$ (respectively, otherwise). We also consider the real quadratic order with conductor $2$ in $\mathbb{Q}(\sqrt{p_1p_2})$.

math.NT↗