Yoshihiro Ônishi

Last modified: March 16, 2017

Crescunt disciplinae lente tardeque, per varios errores sero perventiur ad veritatem, omnia praeparata esse debent diurno et assiduo labore ad introitum veritatis novae; jam illa, certo temporis momento, divina quadam necessitate coacta emergit .....
(Science grows slowly and gently; reaching the truth by a variety of errors. One must prepare the introduction of a new idea through long and diligent labour; then, at a given moment, it emerges as if compelled by a divine necessity .....)
[ From C.G. Jacobi's lecture on being admitted to the Faculty of the University of Königsberg, July 7, 1832) Math. Ann. 56(1903)252 ]

Table of Contents

Educational Background

Research Interests


[ Main publications ]
  1. Y. Ônishi: Arithmetical power series expansion of the sigma function for a plane curve.
    (2017), to appear in   Proc. of the Edinburgh Math. Soc.

  2. 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)

  3. 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 )

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

  5. 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 )

  6. 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) ( collected PDF file )

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

  8. 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 )

  9. 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 )

  10. 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 )

  11. 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

  12. 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, 5th June 2012),

  13. 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 )

  14. Y. Ônishi: Determinant expressions for hyperelliptic functions,
    (with an Appendix by Shigeki Matsutani: Connection of The formula of Cantor and of Brioschi-Kiepert type),
    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.)

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

  16. 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

  17. 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.

  18. 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.

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

  20. 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).

  21. 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.

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

  23. 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: Hurwitz integrality of expansion at the origin of the sigma function for a plane Miura curve (2014, in Japanese : PDF file )

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

  3. 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)

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

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

  6. 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)

  7. 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 ).

  8. 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 ).

  9. 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 ).
[ Ph.D. Thesis ]

[ Conferences ]

Contact Information

E-mail:     yonishi ? meijo-u ? ac ? jp
Address: Department of Mathematics
Faculty of Science and Technology
Meijo University
Shiogamaguchi 1-501, Tenpaku-ku, Nagoya, 468-8052
Office: Building 11, room 303(access and maps)
Phone: +81-(0)52 838-2281

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