with Prof. Don Zagier(Max-Planck-Institut, Bonn, Germany)
Zeta Quantum Research Institute. @^@
Strike while the watermelon is COOL !!
2009.@^@
| R E S E A R C H |
| P A P E R S | |
| (single) |
A conjecture on coincidence among the zeta functions
associated with the space of binary cubic forms, Amer. J. Math. 119 (1997), 1083-1094. |
| (single) | A generalization of the duality and sum formulas on the multiple
zeta values, J. Number Theory 74 (1999), 39-43. |
| with Don Zagier | Multiple zeta values of fixed weight, depth, and height;,
Indag. Math. 12 (2001), 483-487. |
| with Michael Hoffman |
Relations of multiple zeta values and their algebraic expression,
J. Algebra 262 (2003), 332-347. |
| (single) | Sum relations for multiple zeta values, in Zeta functions, Topology, and Quantum Physics
, Dev. Math. 14 (2005), 131-144, Springer. |
| with Takashi Aoki |
Sum relations for multiple zeta values and connection formulas
for the Gauss hypergeometric functions [math.NT/0307264]
, Publ. RIMS Kyoto Univ. 41 (2005), 329-337. |
| with Noriko Wakabayashi | Cyclic sum of multiple zeta values
, Acta Arith. 123 (2006), 289-295. |
| with Takeshi Goto | Perfect numbers, cyclotomic numbers and ABC conjecture
, Trans. Japan Soc. for Industrial and Applied Math. 16 (2006), 187-195. |
| with Yusuke Chishiki and Takeshi Goto | On the largest prime divisor of an odd harmonic number
, Math. Comp. 76 (2007), 1577-1587. |
| with Jun-ichi Okuda | On the sum formula for the $q$-analogue of non-strict multiple zeta values
, Proc. Amer. Math. Soc. 135 (2007), 3029-3037. |
| with Takeshi Goto | Odd perfect numbers have a prime factor exceeding 10^8
, Math. Comp. 77 (2008), 1859-1868. |
| with Takashi Aoki and Yasuhiro Kombu | A generating function for sums of
multiple zeta values and its applications
, Proc. Amer. Math. Soc. 136 (2008), 387-395. |
| with Wadim Zudilin |
Zeta stars
, Commun. Number Theory Phys. 2 (2008), 325-347. |
| with Takashi Taniguchi and Satoshi Wakatsuki |
Relations among Dirichlet series whose coefficients are classs numbers of binary cubic forms
, Amer. J. Math. 131 (2009), 1525-1541. |
| with Masanobu Kaneko | "On a kind of duality of multiple zeta-star values"
, Int. J. Number Theory, to appear. |
| with Takashi Aoki and Noriko Wakabayashi | "On generating functions of multiple zeta values
and generalized hypergeometric functions"
, Manuscripta Math., to appear. |
| with Jun-ichi Okuda and Wadim Zudilin | "Cyclic q-MZSV sum" , submitted. |
| with Takashi Taniguchi | "Relations among Dirichlet series whose coefficients are classs numbers of binary cubic forms II" , submitted. |
| with Kentaro Ihara, Jun Kajikawa and Jun-ichi Okuda | "Multiple zeta values vs. Multiple zeta-star values" , submitted. |
| with Yoshitaka Sasaki and Chika Yamazaki | "On exponential polynomials and quantum computing" , preprint. |
| (single) | "On certain properties of self-complementary graphs", in preparation. |
| with Noriko Wakabayashi | "On basic properties of poly-Bernoulli numbers", in preparation. |
| with Kumi Kobata | "On certain properties of di-graphs", in preparation. |
| (single) | "On the values of Arakawa-Kaneko zeta function", in preparation. |
| with Takashi Aoki, Shuzo Izumi and Manabu Ozaki | "A formula for ideal lattices of general commutative rings" , preprint. |
| with Gunther Cornelissen | "On certain multiple zeta series", in preparation. |
| (single) | A proof of the cyclic sum conjecture for multiple zeta values, preprint (Max-Planck-Institut PREPRINT SERIES 2000). |
| P R O C E E D I N G S | |
| (single) | Zeta functions of binary cubic forms, History and Prospect, Kyotodaigaku Surikaisekikenkyusho Koukyuroku 924 (1995), 134-152. |
| (single) | Relations among multiple zeta values, Proc. of 5th Summer School on Number Theory (1997), 197-204. |
| (single) | Multiple zeta values and a zeta function related to poly-Bernoulli numbers, Proc. of 3rd. Sympos. on Number Theory at Tsudajyuku Univ., (1998), 98-107. |
| (single) | Certain family of relations among multiple zeta values, Proc. of 15th Sympos. on Alg. Combin. Theory, (1998), 222-231. |
| (single) | Multiple zeta values and Arakawa-Kaneko's zeta function, Waseda Univ. Proc. of Sympos. on Number Theory, vol.X, (1999), 57-66. |
| (single) | Special values of multiple zeta function and Arakawa-Kaneko's zeta function, Proc. of 16th Sympos. on Alg. Combin. Theory, (1999), 38-46. |
| (no longer updated...) | ....... |
| T H E S E S | |
| Master Thesis | Study of the zeta functions associated with the space of binary cubic forms, Osaka Univ. (1995). |
| Doctoral Thesis | A generalization of the duality and the sum formula on the multiple zeta values, Osaka Univ. (1998). |
| I N T E R E S T S | |
| Current Research |
Binary cubic forms and cubic fields, Zeta functions associated with certain regular irreducible prehomogeneous vector spaces, Q-algebra of multiple zeta values, Perfect and harmonic numbers, Bernoulli numbers and its generalizations, Quantum computation. |
| Research Interests | Siegel modular forms and Jacobi forms, Symmetry and special values of zeta functions, Invariant theory, Graph theory. |