* Last modified: March 16, 2017*

Japanese

(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
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- 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.

- Y. Ônishi:
Arithmetical power series expansion of the sigma function for a plane curve.

(2017),*to appear in*Proc. of the Edinburgh Math. Soc.

- 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)

- 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 )

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

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

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

Theory of heat equations for sigma functions. ( 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

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