Research theme for competitive and other funds (15)：
2016 - 2019 Research on characterization of the fundamental function sigma in the theory of Abelian functions via heat equations and general addition formulae
2013 - 2016 Construction of concrete theory of Abelian functions focusing the multivariate sigma functions
2011 - 2015 Difference equations related with higher genus algebraic curves
2010 - 2012 Elaborate construction of a concrete theoryof Abelian functions
2007 - 2009 Research toward to construct a concrete theory of Abelian functions
2004 - 2007 Relation between automorphic forms and zeta functions associated with prehomogeneous vector spaces
2004 - 2006 Research on determinantal formulae and Bernoulli-Hurwitz numbers in the theory of Abelian functions
2003 - 2005 The search for the structure which can appear in singular limits of reaction-diffusion systems
2000 - 2002 Research on products formulae for special values of Abehan functions
1998 - 1999 Researches on the parallel queues in use the Computer algebra system REDUCE
1997 - 1998 Researches on the classification of von Neumann algebras by selfdual cones and operator inequalities
1996 - 1996 非可換Lp空間における完全正値写像の研究
1995 - 1995 ガウスの和の積表示とテ-タ関数の積公式
1994 - 1994 ノイマン環の自己準同型とその応用について
1993 - 1993 相乗りタクシーの解析
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Papers (9)：
Y. Onishi, F. Sairaiji. Arithmetic over the Gaussian number field on a certain family of elliptic curves with complex multiplication. RIMS Kôkyûroku Bessatsu. 2021. 1-22
John Chris Eilbeck, Yoshihiro Onishi. Recursion relations on the power series expansion of the universal Weierstrass sigma function. RIMS Kôkyûroku Bessatsu. 2020. 78. 77-98
Yoshihiro Onishi. Arithmetical power series expansion of the sigma function for a plane curve. Proceedings of the Edinburgh Mathematical Society. 2018. 61. 4. 995-1022
Yoshihiro Ônishi. Generalized Bernoulli-Hurwitz numbers and the universal Bernoulli numbers. Russian Mathematical Surveys. 2011. 66. 5. 871-932
J. Chris Eilbeck, Matthew England, Yoshihiro Ônishi. Some New Addition Formulae for Weierstrass Elliptic Functions. 2012
Onishi Y. Frobenius-Stickelberger-Type Formulae for Purely $d$-gonal Curves with Unique Point at Infinity(Algebraic Number Theory and Related Topics). RIMS Kokyuroku. 2006. 1521. 126-138
Victor Z. Enolskii, Shigeki Matsutani, Yoshihiro Ônishi. The addition law attached to a stratification of a hyperelliptic Jacobian variety. 2005
ON POWERS OF MATRICES PRESERVING A SELF-DUAL CONE (Role of Operator Inequalities in Operator Theory). 2005. 1427. 54-64
Yoshihiro Ônishi. Abelian functions for trigonal curves of degree four and determinantal formulae in purely trigonal case. 2005
