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Affiliation |
Faculty of Education Mathematics education |
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Title |
Associate Professor |
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Related SDGs |
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YAMAGUCHI Yuka
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Research Areas 【 display / non-display 】
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Natural Science / Mathematical analysis / 特殊関数
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Natural Science / Applied mathematics and statistics / 多変量解析
Education 【 display / non-display 】
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Kyushu University
2015.4 - 2018.3
Country：Japan
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Kyushu University
2012.4 - 2015.3
Country：Japan
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Kyushu University
2008.4 - 2012.3
Country：Japan
Papers 【 display / non-display 】
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A q-analogue of Gosper’s strange evaluation of the hypergeometric series Reviewed
Yamaguchi Y.
Ramanujan Journal 69 ( 3 ) 2026.3
Authorship：Lead author, Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：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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Basic hypergeometric identities derived from three-term relations Reviewed
Yamaguchi Y.
Ramanujan Journal 69 ( 2 ) 2026.2
Authorship：Lead author, Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：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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Group determinants and invariant rings Reviewed
Yamaguchi Y., Yamaguchi N.
Communications in Algebra 2026.2
Authorship：Lead author Language：English Publishing type：Research paper (scientific journal) Publisher：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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Integer group determinants of order 16 Reviewed
Yamaguchi Y., Yamaguchi N.
Ramanujan Journal 65 ( 3 ) 1459 - 1474 2024.11
Authorship：Lead author Language：English Publishing type：Research paper (scientific journal) Publisher：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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Integer group determinants for abelian groups of order 16 Reviewed
Yamaguchi Y., Yamaguchi N.
Hiroshima Mathematical Journal 54 ( 3 ) 359 - 373 2024.11
Authorship：Lead author Language：English Publishing type：Research paper (scientific journal) Publisher：Hiroshima Mathematical Journal
For any positive integer n, let C<inf>n</inf> be the cyclic group of order n. We determine all possible values of the integer group determinant of C<inf>4</inf> × C<sup>2</sup>2, which is the only unsolved abelian group of order 16.
DOI： 10.32917/h2023012
Grant-in-Aid for Scientific Research 【 display / non-display 】
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超幾何及びq超幾何級数の隣接関係式から得られる特殊値の全容解明
Grant number：25KJ0266 2025.04 - 2026.03
特別研究員奨励費
Authorship：Principal investigator
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超幾何及びq超幾何級数の隣接関係式から得られる特殊値の全容解明
Grant number：25KJ0266R 2025.04 - 2026.03
特別研究員奨励費
Authorship：Principal investigator