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Yuka Yamaguchi

Publications and source records attributed to Yuka Yamaguchi.

At least 19 recordsLinked to original sources
arXiv2026

Group Permanents of Abelian $p$-Groups and Young Diagrams

We study the number $\Nu(\Per(G_λ))$ of distinct monomials with nonzero coefficients in the group permanent of an abelian $p$-group $G_λ$ associated with a partition $λ$ of a positive integer $N$. First, we derive an explicit formula for $\Nu(\Per(G_λ))$ in terms of the partial column sums of the Young diagram of $λ$. Next, we show that the relative order of the values $\Nu(\Per(G_λ))$ is determined by a lexicographic comparison of the conjugate Young diagrams. Finally, we investigate congruence properties of $\Nu(\Per(G_λ))$ for abelian $p$-groups and establish a criterion involving Wolstenholme primes.

math.RT↗
arXiv2026

A further q-analogue of Gosper's strange series

Recently, the second author [Ramanujan J. 2026] introduced and proved a $q$-series identity that appears to provide the first known $q$-analogue of an evaluation for a ${}_{2}F_{1}$-series known as \emph{Gosper's strange series}. Yamaguchi's derivation of this $q$-analogue relies on three-term relations for ${}_{2}ϕ_{1}$-series along with Heine's transformation of ${}_{2}ϕ_{1}$-series. In this note, we introduce and prove, using a $q$-analogue of a series evaluation technique relying on an Abel-type summation lemma, a further $q$-analogue of Gosper's ${}_{2}F_{1}$-identity that is inequivalent to Yamaguchi's $q$-analogue, and we also apply this technique to construct an alternative and simplified proof of Yamaguchi's $q$-analogue, together with a ${}_{3}ϕ_{2}$-series variant of Heine's $q$-analogue of Gauss's hypergeometric formula, a ${}_{6}ϕ_{5}$-series variant and two ${}_{4}ϕ_{3}$-series variants of the $q$-analogue of Kummer's identity due to Bailey and Daum, along with a $q$-analogue of a result obtained by Cantarini [Ramanujan J. 2022] via Fourier-Legendre theory and related to Ramanujan's first series for $\frac{1}π$.

math.CA↗
arXiv2026

Three-Term Recurrence Relations for Confluent Basic Hypergeometric Series with Applications to q-Bessel Functions

We establish three-term recurrence relations for the ${}_1ϕ_1$ and ${}_0ϕ_1$ basic hypergeometric series involving multiplicative shifts of the parameters and the variable by integer powers of q. The coefficients of these recurrence relations are shown to be uniquely determined by the shift indices and are given explicitly in terms of rational functions. These recurrence relations arise as confluent limits of previously established recurrence relations for the ${}_2ϕ_1$ basic hypergeometric series. As an application, we derive three-term recurrence relations for Jackson's second and third q-Bessel functions. These recurrence relations involve additive shifts in the order and multiplicative q-shifts in the variable, and their coefficients include the known q-Lommel polynomials as special cases.

math.CA↗
arXiv2025

Symmetries of coefficients of three-term relations for basic hypergeometric series

Any three basic hypergeometric series ${}_{2}ϕ_{1}$ whose respective parameters $a, b, c$ and a variable $x$ are shifted by integer powers of $q$ are linearly related with coefficients that are rational functions of $a, b, c, q$, and $x$. This relation is called a three-term relation for ${}_{2}ϕ_{1}$. In this paper, we prove that the coefficients of the three-term relation for ${}_{2}ϕ_{1}$ considered in the author's earlier paper (2022) have ninety-six symmetries, and present explicit formulas describing these symmetries.

math.CA↗
arXiv2025

Basic hypergeometric identities derived from three-term relations

In 2015, Ebisu presented a new method for finding hypergeometric identities based on three-term relations for the ${}_{2} F_{1}$ hypergeometric series. By using this method, he derived almost all of the previously known hypergeometric identities, as well as many new ones. In this paper, we derive several basic hypergeometric identities, including both well-known and not widely known ones, by applying a $q$-analogue of Ebisu's method to three-term relations for the ${}_{2} ϕ_{1}$ basic hypergeometric series.

math.CA↗
arXiv2025

A $q$-analogue of Gosper's strange evaluation of the hypergeometric series

In 1977, Gosper conjectured many strange evaluations of hypergeometric series. One of them is a ${}_{2}F_{1}$-series identity with two free parameters, which was proved by Ebisu (2013), Chu (2017), and Campbell (2023) in different ways. In this paper, we present a $q$-analogue of the ${}_{2}F_{1}$-series identity, along with its generalization, by using three-term relations for the ${}_{2}ϕ_{1}$ basic hypergeometric series.

math.CA↗
arXiv2025

Group Determinants and Invariant Rings

In the study of group determinants, Frobenius introduced certain partial differential operators. This paper presents several results concerning the invariant rings derived from these partial differential operators.

math.RT↗
arXiv2023

Wolstenholme primes and group determinants of cyclic groups

A Wolstenholme prime is a prime number $p \geq 5$ that divides the numerator of the Bernoulli number $B_{p-3}$. A number of equivalent definitions for Wolstenholme primes are known, mostly related to congruences of harmonic sums or binomial coefficients. In this paper, we introduce an equivalent definition of Wolstelholme primes related the number of terms in the group determinant of cyclic groups, and equivalently, the cardinality of certain sets of restricted partitions.

math.NT↗
arXiv2023

A necessary and sufficient condition for a prime to be an integer group determinant of certain $p$-groups

We give a necessary and sufficient condition for a prime to be an integer group determinant for an arbitrary abelian $p$-group of the form ${\rm C}_{p} \times H$, where ${\rm C}_{p}$ is the cyclic group of order $p$. Also, we show that under certain conditions, the integer group determinant of a finite group $G$ that is prime is the integer group determinant of the abelianization of $G$. As a result, we know that the integer group determinant of a $p$-group that is prime is the integer group determinant of its abelianization.

math.NT↗
arXiv2023

Inequality for the variance of an asymmetric loss

We assume that the forecast error follows a probability distribution which is symmetric and monotonically non-increasing on non-negative real numbers, and if there is a mismatch between observed and predicted value, then we suffer a loss. Under the assumptions, we solve a minimization problem with an asymmetric loss function. In addition, we give an inequality for the variance of the loss.

math.ST↗
arXiv2023

Generalized Dedekind's theorem and its application to integer group determinants

In this paper, we give a refinement of a generalized Dedekind's theorem. In addition, we show that all possible values of integer group determinants of any group are also possible values of integer group determinants of its any abelian subgroup. By applying the refinement of a generalized Dedekind's theorem, we determine all possible values of integer group determinants of the direct product group of the cyclic group of order $8$ and the cyclic group of order $2$.

math.RT↗
arXiv2023

Integer group determinants for abelian groups of order 16

For any positive integer $n$, let ${\rm C}_{n}$ be the cyclic group of order $n$. We determine all possible values of the integer group determinant of ${\rm C}_{4} \times {\rm C}_{2}^{2}$, which is the only unsolved abelian group of order $16$.

math.NT↗
arXiv2022

Remark on Laquer's theorem for circulant determinants

Olga Taussky-Todd suggested the problem of determining the possible values of integer circulant determinants. To solve a special case of the problem, Laquer gave a factorization of circulant determinants. In this paper, we give a modest generalization of Laquer's theorem. Also, we give an application of the generalization to integer group determinants.

math.RT↗