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Minoru Hirose

Publications and source records attributed to Minoru Hirose.

At least 19 recordsLinked to original sources
arXiv2026

Confluence relations for $q$-analogues of multiple zeta values

In this paper, we construct confluence relations for $q$-analogues of multiple zeta values by adapting the classical construction to the $q$-setting. Our construction uses $q$-analogues of multiple polylogarithms depending on an auxiliary variable $z$, functional relations arising from their $q$-differential equations, and the (regularized) limit as $z$ tends to $1$. We prove that the resulting family of relations contains the stuffle product relations and, assuming a certain conjectural identity, the duality relations for both the Bradley--Zhao and Schlesinger--Zudilin models.

math.NT↗
arXiv2026

A unified proof of conjectures on the spaces of multiple $q$-zeta values

We prove two conjectures on the spaces generated by multiple $q$-zeta values. More precisely, we show that the spaces $Z_q^{\mathrm{o}}$ and $Z_{q,1}^{\mathrm{o}}$ already generate the larger spaces $Z_q$ and $Z_{q,1}$, respectively. Our result is stronger than the equality of $\mathbb{Q}$-vector spaces: for every generator in the larger spaces, we construct an explicit expression with integer coefficients in terms of the smaller generating families. We first establish these formulas at the finite level, where suitable finite $q$-analogues admit recursive descriptions through generating series, and then pass to the infinite limit.

math.NT↗
arXiv2026

Conjectural duality for iterated $q$-integrals on $\mathbb{P}^{1}$ minus four generic points

We propose a conjectural $q$-analogue of the classical duality for iterated integrals on $\mathbb{P}^{1}$ minus four points, arising from the involutive M\"{o}bius transformation which exchanges the four marked points in pairs. To this end, we introduce iterated $q$-integrals with position-dependent $q$-shifts of the parameters and define a functional on admissible words in the six pairwise letters. The conjecture states that this functional is invariant under a natural anti-automorphism of the word algebra. We relate the conjecture to Yamamoto's duality for one-variable multiple $q$-polylogarithms. Finally, we prove the conjecture in several special cases.

math.NT↗
arXiv2026

Systematic Investigation of Acceptor Removal in HPK LGADs with Modified Gain Layers

Low-Gain Avalanche Diodes (LGADs) are fast silicon sensors with internal charge multiplication and are key candidates for precision timing layers in future high-energy hadron colliders. Their operation in harsh radiation environments, however, is limited by acceptor removal in the gain layer, which reduces the active acceptor concentration and degrades the internal electric field required for avalanche multiplication. Improving the radiation tolerance of the gain layer is therefore essential for future 4D tracking applications. In this work, we investigated several LGAD prototypes produced in collaboration with Hamamatsu Photonics K.K. (HPK), featuring modified gain-layer designs, including oxygen-modified, carbon-implanted, and boron--phosphorus compensated structures. The sensors were studied after proton and reactor-neutron irradiation. Radiation tolerance was characterized using the acceptor-removal coefficient extracted from IV measurements and the operation voltage required to recover the timing performance after irradiation. The results show that carbon implantation is the only approach among those studied here that provides a clear improvement in radiation tolerance. In contrast, neither oxygen-related modification, including the Partially Activated Boron (PAB) approach, nor gain-layer compensation alone yields a significant improvement, and the compensated carbon-implanted structure shows no clear advantage over the carbon-only case. In addition, the acceptor-removal coefficient is found to depend on the irradiation particle type and energy.

physics.ins-det↗
arXiv2026

Iterated beta integrals

We introduce iterated beta integrals, a new class of iterated integrals on the universal abelian covering of the punctured projective line that unifies hyperlogarithms and classical beta integrals while preserving their fundamental properties. We establish various analytic properties of these integrals with respect to both the exponent parameters and the main variables. Their key feature is invariance under simultaneous translation of the exponent parameters, which generates relations between integrals over possibly different coverings. This mechanism recovers notable identities for multiple zeta values and variants -- including Zagier's 2-3-2 formula, Murakami's $t$-value analogue, Charlton's $t$-value analogue, Zhao's $2$-$1$ formula, and Ohno's relation -- and also yields new relations, such as a proof of a Galois descent phenomenon for multiple omega values.

math.NT↗
arXiv2025

The $\mathbb{Z}$-module of multiple zeta values is generated by ones for indices without ones

We prove that every multiple zeta value is a $\mathbb{Z}$-linear combination of $\zeta(k_1,\dots, k_r)$ where $k_i\geq 2$. Our proof also yields an explicit algorithm for such an expansion. The key ingredient is to introduce modified multiple harmonic sums that partially satisfy the relations among multiple zeta values and to determine the structure of the space generated by them.

math.NT↗
arXiv2024

Ohno relation for regularized refined symmetric multiple zeta values

The Ohno relation is one of the most celebrated results in the theory of multiple zeta values, which are iterated integrals from $0$ to $1$. In a previous paper, the authors generalized the Ohno relation to regularized multiple zeta values, which are non-admissible iterated integrals from $0$ to $1$. Meanwhile, Takeyama proved an analogue of the Ohno relation for refined symmetric multiple zeta values, which are iterated integrals from $0$ to $0$. In this paper, we generalize Takeyama's result to regularized refined symmetric multiple zeta values, which are non-admissible iterated integrals from $0$ to $0$.

math.NT↗
arXiv2024

Mixed Tate motives and cyclotomic multiple zeta values of level $2^n$ or $3^n$

Let $N$ be a power of $2$ or $3$, and $\mu_{N}$ the set of $N$-th roots of unity. We show that the ring of motivic periods of Mixed Tate motives over $\mathbb{Z}[\mu_{N},\frac{1}{N}]$ is spanned by the motivic cyclotomic multiple zeta values of level $N$. This implies that the action of the motivic Galois group of mixed Tate motives over $\mathbb{Z}[\mu_{N},\frac{1}{N}]$ on the motivic fundamental group of $\mathbb{G}_{m}-\mu_{N}$ is faithful. This is a generalization of the known results for $N\in\{1,2,3,4,8\}$ by Deligne and Brown. We also discuss cyclotomic multiple zeta values of weight $2$ of other levels.

math.NT↗
arXiv2024

A discretization of the iterated integral expression of the multiple polylogarithm

Recently, Maesaka, Watanabe, and the third author discovered a phenomenon where the iterated integral expressions of multiple zeta values become discretized. In this paper, we extend their result to the case of multiple polylogarithms and provide two proofs. The first proof uses the method of connected sums, while the second employs induction based on the difference equations that discrete multiple polylogarithms satisfy. We also investigate several applications of our main result.

math.NT↗
arXiv2024

Characterization of order structures avoiding three-term arithmetic progressions

It is known that the set of all nonnegative integers may be equipped with a total order that is chaotic in the sense that there is no monotone three-term arithmetic progressions. Such chaotic order must be so complicated that the resulting ordered set cannot be order isomorphic to the set of all nonnegative integers or the set of all integers with the standard order. In this paper, we completely characterize order structures of chaotic orders on the set of all nonnegative integers, as well as on the set of all integers and on the set of all rational numbers.

math.CO↗
arXiv2024

Multitangent functions and symmetric multiple zeta values

In this paper, we give a formula that connects two variants of multiple zeta values; multitangent functions and symmetric multiple zeta values. As an application of this formula, we give two results. First, we prove Bouillot's conjecture on the structures of the algebra of multitangent functions. Second, we prove an analogue of the linear part of Kawashima's relation for symmetric multiple zeta values.

math.NT↗
arXiv2023

Associators in mould theory

By developing various techniques of mould theory and establishing a quasi-involutive reformulation of Drinfeld's associator set, we introduce $\mathsf{GARI}(\mathscr{F})_{\mathsf{as}+\mathsf{bal}}$, a mould theoretic formulation of Drinfeld's associator set. We give a mould-theoretical generalization of the result that associator relations imply double shuffle relations, namely, we explain that $\mathsf{GARI}(\mathscr{F})_{\mathsf{as}+\mathsf{bal}}$ is embedded into Ecalle's set $\mathsf{GARI}(\mathscr{F})_{\mathsf{as}\ast\mathsf{is}}$ which is a mould theoretic version of Racinet's double shuffle set.

math.QA↗
arXiv2023

On a lifting of $t$-adic symmetric multiple zeta values

The $t$-adic symmetric multiple zeta value is a generalization of the symmetric multiple zeta value from the perspective of the Kaneko-Zagier conjecture. In this paper, we introduce a further generalization with a new parameter $s$, which we call the $(s,t)$-adic symmetric multiple zeta value. Then, the $(s,t)$-adic version of the $t$-adic double shuffle relations, duality and cyclic sum formula are established. A finite counterpart of the $(s,t)$-adic symmetric multiple zeta value is also discussed.

math.NT↗
arXiv2023

Multiple zeta-star values for indices of infinite length

In this paper, we consider infinite-length versions of multiple zeta-star values. We give several explicit formulas for the infinite-length versions of multiple zeta-star values. We also discuss the analytic properties of the map from indices to the infinite-length versions of multiple zeta-star values.

math.NT↗
arXiv2023

Integral expressions for Schur multiple zeta values

Nakasuji, Phuksuwan, and Yamasaki defined the Schur multiple zeta values and gave iterated integral expressions of the Schur multiple zeta values of the ribbon type. This paper generalizes their integral expressions to the ones of more general Schur multiple zeta values having constant entries on the diagonals. Furthermore, we also discuss the duality relations for Schur multiple zeta values obtained from the integral expressions.

math.NT↗