Yoshihiro Ônishi

Table of Contents

• Educational Background
• Research Interests
• Ilustration
• Publications
• Conferences
• TeX Tips
• The sigma functions in genus one and two
• An example for non-Galois complex multiplication
• A table over-viewing Bernoulli-Hurwitz-type numbers
• Contact Information

26. J. C. Eilbeck, J. Gibbons, Y. Ônishi, and S. Yasuda:
    Theory of heat equations for sigma functions.
    Glasgow Math. J. (FirstView) (DOI:10.1017/S0017089524000417)   ( PDF file ) ( arxiv.org )
    
    
25. Y. Ônishi, and F. Sairaiji: Arithmetic over the Gaussian number field on a certain family of elliptic curves with complex multiplication.
    (to appear in RIMS Kôkyũroku Bessatsu) ( PDF file )
    
    
24. 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
    
    
23. 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)
    
    
22. 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)
    
    
21. 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)
    
    
20. Y. Ônishi: Generalized Bernoulli-Hurwitz numbers and the universal Bernoulli numbers.
    Russian Mathematical Surveys, 66:5 (2011) 871-932
    (DOI:10.1070/rm2011v066n05abeh004763)
    Ёшихиро Ониши: “Обобщенные числа Бернулли–Гурвица и универсальные числа Бернулли”, УМН, 66:5(401) (2011), 47–108; (PDF file)
    (The corollary 3.3 (see Section 3.5) has an error. Its detailed description is in preparation. )
    
    
19. 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 )
    
    
18. 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 )
    
    
17. 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
    
    
16. 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 )
    
    
15. 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 )
    
    
14. 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 )
    
    
13. 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),
    
    
11. 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 )
    
    
10. Y. Ônishi: Determinant expressions for hyperelliptic functions,
    Proc. Edinburgh Math. Soc., 48 (2005) 705-742.
    (Errata PDF file ), (In this paper a final form of the formula of Frobenius-Stickelberger type for any hyperelliptic curve is proved.)
    
    
9. Y. Ônishi: Determinantal expressions for hyperelliptic functions in genus three,
   Tokyo J. Math., 27 (2004) 299-312, ( PDF file ).
   
   
8. 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
   
   
7. 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.
   
   
6. 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.
   
   
5. Y. Ônishi: Determinant expressions for Abelian functions in genus two,
   Glasgow Math. J., 44 (2002) 353-364, ( PDF file ).
   
   
4. 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).
   
   
3. 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.
   
   
2. Y. Ônishi: On the Galois group corresponding to the formula of Grant,
   Comm. Math. Univ. Sancti Pauli, 49 (1993) 37-48.
   
   
1. K. Horie and Y. Ônishi: The existence of certain infinite families of imaginary quadratic fields,
   J. reine und angew. Math., 390 (1988) 97-113.
   ( I only learned through this paper on idea and knowledge of Professor Horie. I deeply appreciate his affection of including me as a coauthor. )

19. Y. Ônishi: A suggestion for correcting Section 5 of "J.W.S. Cassels: Arithmetic on Curves of Genus 1. IV".
    ( PDF file )
    
    
18. Y. Ônishi: The convergence radii of series expansions of functions on an algebraic curve.
    ( PDF file )
    
    
17. 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 )
    
    
16. 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 )
    
    
15. J.C.Eilbeck, J.Gibbons, Y.Ônishi, and E.Previato:
    Explicit realization of Coble's hypersurfaces in terms of multivariate ℘-functions. ( PDF file )
    
    
14. 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 ) contains Japanese (This is improved to no.17)
    
    
13. 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 ) contains Japanese
    
    
12. 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 ) contains Japanese
    
    
11. Y. Ônishi: An example of the example by Hecke described in Shimura-Taniyama's book. ( PDF file , in Japanese)
    
    
10. Y. Ônishi: On Weierstrass' paper ''Zur Theorie der elliptischen Functionen.'' ( PDF file )
    
    
9. 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 )
   
   
8. Y. Ônishi: Universal elliptic functions.
   (English : PDF file ) (Japanese : PDF file )
   
   
7. 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)
   
   
6. 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)
   
   
4. 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)
   
   
3. 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 ).
   
   
2. 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 ).
   
   
1. 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
  

• International Conference on Jacobian varieties, Abelian functions, and Kummer surfaces