論文 (2017.3.16 現在 )


[ レフェリー付きの雑誌に掲載された（される）もの ]
  1. J.C. Eilbeck, and Y. Ônishi: Recursion relations on the power series expansion of the universal Weierstrass sigma function.
    RIMS Kôkyûroku Bessatsu, 2019 (PDF file)

  2. Y. Ônishi: Arithmetical power series expansion of the sigma function for a plane curve.
    Proc. of the Edinburgh Math. Soc., 61:4(Nov. 2018) 995-1022
    https://doi.org/10.1017/S0013091517000463

  3. J. C. Eilbeck, M. England, and Y. Ônishi: Some new addition formulae for Weierstrass elliptic functions.
    Proc. R. Soc. A 470(2014)14 pages (DOI: 10.1098/rspa.2014.0514) (PDF file)

  4. J.Gibbons, S.Matsutani, and Y.Ônishi: Relationship between the prime form and the sigma function for some cyclic (r,s) curves.
    Journal of Physics A: Mathematical and Theoretical, Vol. 46:17(2013) (in print) ( PDF file )

  5. Y. Ônishi: Generalized Bernoulli-Hurwitz numbers and the universal Bernoulli numbers.
    Russian Mathematical Surveys, 66:5(2011)871-932 ( PDF file )

  6. Matthew England, J. Chris Eilbeck and Y. Ônishi: Abelian Functions associated with genus three algebraic curves.
    London Math. Soc. Jour. of Computation and Math., 14(2011)291-326 ( PDF file )

  7. Y. Ônishi: Determinant formulae in Abelian functions for a general trigonal curve of degree five.
    Computational Methods and Function Theory, 11:2(2011)547-574 (special volume : "Constructive methods for compact Riemann surfaces in applications") (CMFT site) ( PDF file )

  8. J.C. Eilbeck, S. Matustani and Y. Ônishi: Addition formula for Abelian functions associated with specialized curves.
    Phil.Trans. Royal Society A, 369(2011)1245-1263

  9. Y. Ônishi: Congruence relations connecting Tate-Shafarevich groups with Hurwitz numbers.
    Interdisciplinary of Information Sciences, 16:1(2010)71-86 (= Proceedings of Japan-Korea Joint Seminar on Number Theory and Related Topics 2008) ( PDF file )

  10. Y. Ônishi: Abelian functions for trigonal curves of dgree four and determinantal formulae in purely trigonal case.
    International Journal of Mathematics, 20:4(2009)427-441 ( PDF file )

  11. V.Z. Enolskii, S. Matsutani and Y. Ônishi:
    The addition law attached to a stratification for a hyperelliptic Jacobian variety.
    Tokyo Journal of mathematics, 31(2008)27-38 ( PDF file )

  12. S. Baldwin, J. C. Eilbeck, J. Gibbons, and Y. Ônishi:
    Abelian functions for cyclic trigonal curves of genus 4,
    J. Geom. Phys.,58:4(2008)450-467 math.AG/0612654, DOI: 10.1016/j.geomphys.2007.12.001

  13. J.C. Eilbeck, V.Z. Enol'skii, S. Matustani, Y. Ônishi, and E. Previato:
    Abelian functions for trigonal curves of genus three.
    International Mathematics Research Notices, 2008:1(2008)102-139
    (http://arxiv.org/abs/math.AG/0610019) ( corrected PDF file , Uploaded, 16th October 2006).

  14. J.C. Eilbeck, V.Z. Enol'skii, S. Matustani, Y. Ônishi, and E. Previato:
    Addition formulae over the Jacobian pre-image of hyperelliptic Wirtinger varieties,
    J. reine und angew. Math.,619(2008)37-48 ( PDF file )

  15. Y. Ônishi: Determinant expressions for hyperelliptic functions,
    Proc. Edinburgh Math. Soc., 48(2005)705-742. ( PDF file , Last update 2005.3.11).
    (Errata PDF file ), (In this paper a final form of the formula of Frobenius-Stickelberger type for any hyperelliptic curve is proved.)

  16. Y. Ônishi: Determinantal expressions for hyperelliptic functions in genus three,
    Tokyo J. Math., 27(2004)299-312, ( PDF file ).

  17. Y. Ishikawa, Y. Miura and Y.Ônishi:
    Inqualities for matrices preserving a self-dual cone M_2(R)^+,
    Far East J. Math. Sci., 16(2005)63-72

  18. S. Matsutani and Y. Ônishi:
    Wave-Particle complementarity and reciprocity of Gauss sums on Talbot effects,
    Foundations of Physics Letters, 16:4(2003)325-341.

  19. S. Matsutani and Y. Ônishi:
    On the moduli of quantized elastica in P and KdV flows: Study of hyperelliptic curves as an extension of Euler's perspective of elastica I,
    Reviews in Math. Physics, 15:6(2003)559-628.

  20. Y. Ônishi: Determinant expressions for Abelian functions in genus two,
    Glasgow Math. J., 44(2002)353-364, ( PDF file ).

  21. Y. Ônishi: Complex multiplication formulae for hyperelliptic curves of genus three, Tokyo J. Math., 21(1998)381-431;
    Correction and supplement ( PDF file );
    Corrected files ( PDF file , Last update 2004.3.6).

  22. S. Ishiwata, S. Matsutani and Y. Ônishi:
    Localized state of hard core chain and cyclotomic polynomial: hard core limit of diatomic Toda lattice,
    Physics Letters A, 231(1997)208-216.

  23. Y. Ônishi: On the Galois group corresponding to the formula of Grant,
    Comm. Math. Univ. Sancti Pauli, 49(1993)37-48.

  24. K. Horie and Y. Ônishi: The existence of certain infinite families of imaginary quadratic fields,
    J. reine und angew. Math., 390(1988)97-113.
[ Preprints and other writings ]
  1. Y. Ônishi:
    Further generalization of the addition formula of Frobenius-Stickelberger to higher genus Abelian functions.
    "Muliple sine functions and their application", Kobe University, 5-7, February 2020
    ( PDF file )

  2. Y. Ônishi:
    Vanishing elliptic Gauss sums and Bernoulli-Hurwitz type numbers.
    "RIMS conference, Algebraic number theory and Related Topics 2019", RIMS, 9-13, December 2019
    ( PDF file )

  3. J.C.Eilbeck, J.Gibbons, Y.Ônishi, and E.Previato:
    Explicit realization of Coble's hypersurfaces in terms of multivariate ℘-functions. ( PDF file )

  4. Y. Ônishi:
    Vanishing elliptic Gauss sums and Bernoulli-Hurwitz type numbers.
    "The 40th Aichi Number theory Seminar", Aichi Institute of Technology, 30, March 2019
    ( PDF file ) may contains Japanese

  5. Y. Ônishi:
    A recursion system on the expansion coefficients of the sigma function for a higher genus curve.
    "The 23rd Conference on Number theory at Waseda University", Waseda Univ., 13-15, March 2019
    ( PDF file ) may contains Japanese

  6. Y. Ônishi:
    On a generalization of the theory of heat equations for the Weierstrass sigma function to higher genus case.
    "Mathematical structures observed from the theory of integrable systems and its applications" organized by Shinsuke Iwao, RIMS, 6-8, Sep. 2018
    ( PDF file ) may contains Japanese

  7. J. C. Eilbeck, J. Gibbons, Y. Ônishi, and S. Yasuda:
    Theory of heat equations for sigma functions. ( PDF file ) ( arxiv.org )

  8. Y. Ônishi: 志村・谷山著 『近代的整数論』に挙げられてゐる Hecke の例の具体例.
    ( PDF file )

  9. Y. Ônishi: On Weierstrass' paper ''Zur Theorie der elliptischen Functionen.'' ( PDF file )

  10. Y. Ônishi: New addition formulae for Weierstrass elliptic functions and for higher genus Abelian functions.
    "Japan-Korea number theory seminar", Keio Univ., 19-22, Dec. 2014
    "Curves, moduli, and integrable systems", Tsuda college, 17-19, Feb. 2015
    ( slide of these talks )

  11. Y. Ônishi: Universal elliptic functions.
    (English : PDF file ) (Japanese : PDF file )

  12. Frobenius-Stickelberger-type formulae for general curves.
    "The higher-genus sigma function and applications", ICMS at Edinburgh, 11-15, Oct. 2010
    (slide of this talk), (poster on this talk), (slides of speakers)

  13. Y. Ônishi: The main congruences on generalized Bernoulli-Hurwitz numbers for the curves of cyclotomic type.
    ( PDF file )

  14. Y. Ônishi: Integrality of coefficients of division polynomials for elliptic Functions.
    ( PDF file , Last update 14th Feb. 2011)

  15. S. Matsutani and Y. Ônishi: Determinant expressions in Abelian functions for purely pentagonal curves of degree six.
    ( PDF file , Last update 29th January 2006); (Japanese : PDF file , Last update 21st October 2007)

  16. Y. Ônishi: Kummer's original type congruence relation for the universal Bernoulli numbers.
    (The results themselves of this paper are contained in the published paper no.20 above. )
    ( PDF file ); (Japanese : PDF file ).

  17. Y. Ônishi: Generalizations to hyperelliptic curves of the division polynomials of elliptic curves and thier determinant expressions.
    Proceedings of the work shop "Cryptography, and its founded theories on algebraic curves II", held at Chuo University, (2001)121-140.
    (The author conjectured a final form of the formula of Frobenius-Stickelberger type for any hyperelliptic curves. )
    (Japanese : PDF file ).
  18. Y. Ônishi: On a generalization of Jacobi's derivative formula to hyperelliptic curves.
    (This is a personal note and does not contain new results.)
    ( PDF file ),

[ 博士（理学）学位論文 ]

[ その他の主な寄稿 ]
  1. Explicit realization of Coble's hypersurfaces in terms of multivariate ℘-functions.
    早稲田大学，整数論研究集会 (2013 年 3 月 16 〜 3 月 18 日) 報告集, (2013)??-??.

  2. Frobenius-Stickeberger-type formulae for purely d-gonal curves with unique point at infinity,
    京都大学数理解析研究所講究録 Vol.1521「代数的整数論とその周辺」(2006)27-38.

  3. 大西良博： 円分型代数函数版 Bernoulli-Hurwitz 数と普遍 Bernoulli 数の理論.
    「2004 数論セミナー 静岡」(2005)1-91. ( PDF file )

  4. 大西良博： 普遍 Bernoulli 数に対する Kummer の原論文型合同式.
    「2003 数論セミナー 静岡」(2004)111-126. ( PDF file ) (English : PDF file ).

  5. Abel 函数の新理論, 特に 行列式表示公式と Bernoulli-Hurwitz 数の拡張について,
    早稲田大学，整数論研究集会 (2004 年 3 月 17 〜 3 月 19 日) 報告集, (2004)27-37.

  6. 普遍 Bernoulli 数と円分型代数函数版 Bernoulli-Hurwitz 数,
    京都大学数理解析研究所講究録 Vol.1376「代数的整数論とその周辺」(2004)50-60.

  7. 大西良博: 楕円曲線の等分多項式の超楕円曲線への一般化とその行列式表示,
    中央大学における Work shop 「暗号理論とそれを支える代数曲線論 第 2 回」の報告集 (2001)121-140. ( PDF file ).

  8. 円分型の超楕円曲線に対する虚数乗法公式,
    早稲田大学理工学総合研究センター 学術支援領域 (数理科学) 研究集会 第十回, 整数論 (早稲田大学, 1999.3.4-6) 報告集, (1999)22-32.

  9. Eisenstein-Grant の積公式の種数 3 への一般化,
    整数論シンポジウム (香川大学, 1993.10.12-16) 報告書, (1994)81-95.

  10. Eisenstein の積公式の種数 2 への一般化,
    数理解析研究所 講究録, 759(1991)198-209.


[ 主な口頭発表 ]
  1. Frobenius-Stickelberger-type formulae for general curves,
    "The higher-genus sigma function and applications", ICMS at Edinburgh, 11-15, Oct. 2010
    (slide of this talk), (poster on this talk), (slides of speakers)

  2. Frobenius-Stickeberger-type formulae for purely d-gonal curves with unique point at infinity,
    「代数的整数論とその周辺」於 : 京都大学数理解析研究所 (2005 年 12 月 5 日 〜 12 月 9 日)

  3. Abel 函数の新理論, 特に 行列式表示公式と Bernoulli-Hurwitz 数の拡張について,
    早稲田大学，整数論研究集会 (2004 年 3 月 17 〜 3 月 19 日)

  4. A New Theory of Abelian Functions --- Determinantal Expressions and Generalized Bernoulli-Hurwitz Numbers ---.
    Glasgow University, All algebra seminar (3rd June 2004)

  5. 普遍 Bernoulli 数と円分型代数函数版 Bernoulli-Hurwitz 数,
    「代数的整数論とその周辺」於 : 京都大学数理解析研究所 (2003 年 12 月 1 日 〜 12 月 5 日).

  6. あるアーベル函数の行列式表示について,
    日本数学会，2000 年, 秋季分科会 (京都大学)