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所属 |
教育学部 数学教育 |
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職名 |
准教授 |
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関連SDGs |
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学歴 【 表示 ／ 非表示 】
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九州大学 数理学府 数理学専攻（博士後期課程）
2015年4月 - 2018年3月
国名：日本国
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九州大学 数理学府 数理学専攻（修士課程）
2012年4月 - 2015年3月
国名：日本国
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九州大学 理学部 数学科
2008年4月 - 2012年3月
国名：日本国
論文 【 表示 ／ 非表示 】
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A q-analogue of Gosper’s strange evaluation of the hypergeometric series 査読あり
Yamaguchi Y.
Ramanujan Journal 69 ( 3 ) 2026年3月
担当区分：筆頭著者, 責任著者 記述言語：英語 掲載種別：研究論文（学術雑誌） 出版者・発行元：Ramanujan Journal
In 1977, Gosper conjectured many strange evaluations of hypergeometric series. One of them is a -series identity with two free parameters, which has since been proved by several researchers using different methods. In this paper, we present a q-analogue of the -series identity, along with a generalization, by using three-term relations for the basic hypergeometric series.
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Group determinants and invariant rings 査読あり
Yamaguchi Y., Yamaguchi N.
Communications in Algebra 2026年2月
担当区分：筆頭著者 記述言語：英語 掲載種別：研究論文（学術雑誌） 出版者・発行元：Communications in Algebra
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.
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Basic hypergeometric identities derived from three-term relations 査読あり
Yamaguchi Y.
Ramanujan Journal 69 ( 2 ) 2026年2月
担当区分：筆頭著者, 責任著者 記述言語：英語 掲載種別：研究論文（学術雑誌） 出版者・発行元：Ramanujan Journal
In 2015, Ebisu presented a new method for finding hypergeometric identities based on three-term relations for the 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 basic hypergeometric series.
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Integer group determinants of order 16 査読あり
Yamaguchi Y., Yamaguchi N.
Ramanujan Journal 65 ( 3 ) 1459 - 1474 2024年11月
担当区分：筆頭著者 記述言語：英語 掲載種別：研究論文（学術雑誌） 出版者・発行元：Ramanujan Journal
Let C<inf>n</inf> and Q<inf>n</inf> denote the cyclic group and the generalized quaternion group of order n, respectively. We determine all possible values of the integer group determinants of C<inf>8</inf>⋊<inf>3</inf>C<inf>2</inf> and Q<inf>8</inf>⋊C<inf>2</inf>, which are the unresolved groups of order 16 (Serrano, Paudel and Pinner also obtained a complete description of the integer group determinants of Q<inf>8</inf>⋊C<inf>2</inf> independently of this paper and presented it a few days earlier than this paper). Also, we give a diagram of the set inclusion relations between the integer group determinants for all groups of order 16
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Wolstenholme primes and group determinants of cyclic groups 査読あり
Reyes-Bustos C., Yamaguchi N., Yamaguchi Y.
Proceedings of the Japan Academy Series A Mathematical Sciences 100 ( 9 ) 51 - 55 2024年11月
記述言語：英語 掲載種別：研究論文（学術雑誌） 出版者・発行元：Proceedings of the Japan Academy Series A Mathematical Sciences
A Wolstenholme prime is a prime number p ≥ 5 that divides the numerator of the Bernoulli number B<inf>p−</inf><inf>3</inf>. A number of equivalent definitions for Wolstenholme primes are known, mainly related to congruences of harmonic sums or binomial coefficients. In this paper, we introduce an equivalent definition of Wolstelholme primes related to the number of terms in the group determinant of cyclic groups, and equivalently, the cardinality of certain sets of restricted partitions.
DOI： 10.3792/pjaa.100.011