Publications

Papers

  1. On the difference between the ordinary height and the canonical height on elliptic curves, Proc. Japan Acad. Ser. A Math. Sci. 82, no. 3, 56-60, (2006).
  2. The difference between the ordinary height and the canonical height on elliptic curves, J. Number Theory 128, 263-279, (2008).
  3. Division polynomials and canonical local heights on hyperelliptic Jacobians, Manuscripta Math. 134, 273-308, (2011).
  4. Valuations of Somos 4 sequences and canonical local heights on elliptic curves, Math. Proc. Cambridge Philos. Soc. 150, 385-397, (2011).
  5. Canonical local heights and multiplication formulas for the Jacobians of curves of genus 2, Acta Arith. 149, 111-130, (2011).
  6. (with Shigenori Uchiyama) The Tate-Lichtenbaum pairing on a hyperelliptic curve via hyperelliptic nets, Pairing-Based Cryptography - Pairing 2012, 218-233, Lecture Notes in Comput. Sci., 7708, Springer, Berlin, 2013.
  7. (with Junichi Yarimizu and Shigenori Uchiyama) The elliptic curve Diffie-Hellman problem and an equivalent hard problem for elliptic divisibility sequences, JSIAM Lett. 6, 5-7, (2014).
  8. (with Akihiko Onishi and Shigenori Uchiyama) A small secret exponent attack on cryptosystems using Dickson polynomials, JSIAM Lett. 7, 41-43, (2015).
  9. Computing the Mordell-Weil Groups of Hyperelliptic Jacobians, Transactions of the Japan Society for Industrial and Applied Mathematics 25, 229-253, (2015), (Japanese).
  10. Counting points on hyperelliptic curves of genus 2 with real models, JSIAM Lett. 11, 1-4, (2019).
  11. (with Masanori Sawa) Discriminants of classical quasi-orthogonal polynomials with application to Diophantine equations, J. Math. Soc. Japan 71, 831-860, (2019).
  12. (with Masanori Sawa) Algebro-geometric aspects of the Christoffel-Darboux kernels for classical orthogonal polynomials, Trans. Amer. Math. Soc. 373, 1243-1264, (2020).
  13. (with Yasuhiro Ishitsuka, Tetsushi Ito, Tatsuya Ohshita, and Takashi Taniguchi) The local-global property for bitangents of plane quartics, JSIAM Lett. 12, 41-44, (2020).

Preprints

  1. (with Hiro-o Tokunaga) A remark on a Nagell-Lutz type statement for the Jacobian of a curve of genus 2 and a (2, 3, 6) quasi-torus decomposition of a sextic with 9 cusps, arXiv:1808.10187.
  2. (with Yasuhiro Ishitsuka, Tetsushi Ito, Tatsuya Ohshita, and Takashi Taniguchi) Periods modulo p of integer sequences associated with division polynomials of genus 2 curves, arXiv:2310.01013.

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