Centers & Labs

RIKEN Center for Advanced Intelligence Project

Mathematical Science Team

Team Leader: Kenichi Bannai (D.Math.Sci)
Kenichi  Bannai(D.Math.Sci)

My main area of research is in Arithmetic Geometry, which is a branch of number theory in the filed of pure Mathematics. My research interest is the development of mathematical tools in order to understand conjectures concerning special values of Hasse-Weil L-functions associated to Algebraic Varieties defined over number fields. I hope to apply these and other mathematical tools to the study of machine learning and artificial intelligence.

Main Research Field

Mathematics

Research Subjects

  • Arithmetic Geometry
  • Machine Learning

Selected Publications

Papers with an asterisk(*) are based on research conducted outside of RIKEN.
  1. *Kenichi Bannai, and Shinichi Kobayashi:
    “Integral structures on p-adic Fourier theory”
    Annales de L'Institut Fourier, Vol. 66 no. 2, 521-550 (2016). DOI: 10.5802/aif.3018.
  2. *Kenichi Bannai, Hidekazu Furusho, and Shinichi Kobayashi:
    “p-adic Eisenstein–Kronecker series for CM elliptic curves and the Kronecker limit formulas”
    Nagoya Math. J. 219, 269-302 (2015). DOI: 10.1215/00277630-2891995.
  3. *Kenichi Bannai, and Guido Kings:
    “p-adic Beilinson conjecture for ordinary Hecke motives associated to imaginary quadratic fields”
    RIMS Kôkyûroku Bessatsu B25: Algebraic Number Theory and Related Topics 2009, eds. T. Ichikawa, M. Kida, T. Yamazaki, 9-30 June (2011).
  4. *Kenichi Bannai, and Guido Kings:
    “p-adic elliptic polylogarithm, p-adic Eisenstein series and Katz measure”
    American J. Math. 132 no. 6, 1609-1654 (2010).
  5. *Kenichi Bannai, and Shinichi Kobayashi:
    “Algebraic theta functions and p-adic interpolation of Eisenstein-Kronecker numbers”
    Duke Math. J. 153 no. 2, 229-295 (2010). DOI: 10.1215/00127094-2010-024.
  6. *Kenichi Bannai, Shinichi Kobayashi, and Takeshi Tsuji:
    “On the de Rham and p-adic realizations of the elliptic polylogarithm for CM elliptic curves”
    Annales scientifiques de l'ENS 43, fascicule 2, 185-234 (2010).
  7. *Kenichi Bannai, and Shinichi Kobayashi:
    “Algebraic theta functions and Eisenstein-Kronecker numbers”
    RIMS Kôkyûroku Bessatsu B4: Proceedings of the Symposium on Algebraic Number theory and Related Topics, eds. K. Hashimoto, Y. Nakajima and H. Tsunogai, 63--78 December (2007).
  8. *Kenichi Bannai:
    “On the p-adic realization of elliptic polylogarithms for CM-elliptic curves”
    Duke Math. J. 113, 193-236 (2002). DOI: 10.1215/S0012-7094-02-11321-0.
  9. *Kenichi Bannai:
    “Syntomic cohomology as a p-adic absolute Hodge cohomology”
    Math. Z. 242/3, 443-480 (2002). DOI: 10.1007/s002090100351.
  10. *Kenichi Bannai:
    “Rigid syntomic cohomology and p-adic polylogarithms”
    J. Reine Angew. Math. 529, 205-237 (2000). DOI: 10.1515/crll.2000.097.