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* Last modified: March 16, 2017*

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(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 ]

- Educational Background
- Research Interests
- Ilustration
- Publications
- Conferences
- TeX Tips
- The sigma functions in genus one and two
- An example for non-Galois complex multiplication
- Contact Information

- Ph.D., 1999, Tokyo Metropolitan University
- Master of Science, 1987, Tokyo Metropolitan University
- Bachelor of Science, 1985, Shizuoka University

- Theory of Abelian Functions, Algebraic Curves
- Theory of Complex Multiplication,
- Algebraic Number Theory,
- Problem of the determination of argument of Gauss sums,
- Extension of Cassels-Matthews formulae.

- J.C. Eilbeck, and Y. Ônishi:
Recursion relations on the power series expansion of the universal Weierstrass sigma function.

RIMS Kôkyûroku Bessatsu, 78(April, 2020) 77-98 (PDF file)

- 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

(**DOI:**10.1017/S0013091517000463)

- J. C. Eilbeck, M. England, and Y. Ônishi:
Some new addition formulae for Weierstrass elliptic functions.

Proceedings of the Royal Society. A 470(2014)14 pages (**DOI:**10.1098/rspa.2014.0051) (PDF file)

- 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) (**DOI:**10.1088/1751-8113/46/17/175203)

- Y. Ônishi: Generalized Bernoulli-Hurwitz numbers and the universal Bernoulli numbers.

Russian Mathematical Surveys, 66:5(2011)871-932

(**DOI:**10.1070/rm2011v066n05abeh004763) ( PDF file )

- 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 )

- 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 )

- 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

- 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 )

- 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 )

- 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 )

- 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

- 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),

- 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 )

- 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.*)

- Y. Ônishi:
Determinantal expressions for hyperelliptic functions in genus three,

Tokyo J. Math., 27(2004)299-312, ( PDF file ).

- 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

- 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.

- S. Matsutani and Y. Ônishi:

On the moduli of quantized elastica inand KdV flows: Study of hyperelliptic curves as an extension of Euler's perspective of elastica I,*P*

Reviews in Math. Physics, 15:6(2003)559-628.

- Y. Ônishi: Determinant expressions for Abelian functions in genus two,

Glasgow Math. J., 44(2002)353-364, ( PDF file ).

- 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).

- 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.

- Y. Ônishi:
On the Galois group corresponding to the formula of Grant,

Comm. Math. Univ. Sancti Pauli, 49(1993)37-48.

- K. Horie and Y. Ônishi:
The existence of certain infinite families of imaginary quadratic fields,

J. reine und angew. Math., 390(1988)97-113.

- Y. Ônishi, and F. Sairaiji:
Arithmetic over the Gaussian number field on a certain family of elliptic curves with complex multiplication.

(submitted to RIMS Kôkyũroku Bessatsu) ( PDF file )

- 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 )

- 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 )

- J.C.Eilbeck, J.Gibbons, Y.Ônishi, and E.Previato:

Explicit realization of Coble's hypersurfaces in terms of multivariate ℘-functions. ( PDF file )

- 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 (This is improved to no.17)

- 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

- 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

- J. C. Eilbeck, J. Gibbons, Y. Ônishi, and S. Yasuda:

Theory of heat equations for sigma functions. ( PDF file ) ( arxiv.org )

- Y. Ônishi:
An example of the example by Hecke described in Shimura-Taniyama's book.
( PDF file , in Japanese)

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

- 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 )

- Y. Ônishi:
Universal elliptic functions.

(*English*: PDF file ) (*Japanese*: PDF file )

- 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)

- Y. Ônishi:
The main congruences on generalized Bernoulli-Hurwitz numbers for the curves of cyclotomic type.

( PDF file )

- Y. Ônishi:
Integrality of coefficients of division polynomials for elliptic Functions.

( PDF file , Last update 14th Feb. 2011)

- 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)

- 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 ).

- 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 ).

- 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 ).

- Complex multiplication formulae for hyperelliptic curves
of cyclotomic type and the corresponding Galois groups.

June, 1999, Tokyo Metropolitan University

[ Conferences ]

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