Department of Mathematics,
Graduate School of Science, Kobe University
Division : Algebra
Building B, Room 425

Personal Website

Research Field : Algebraic Number Theory: Number theory for prehomogeneous vector spaces of parabolic type and their zeta functions

Research Summary : In number theory, we often encounter "zeta functions" which are complex analytic functions, and it becomes important to understand their analytic properties. "Prehomogeneous vector space (PV)" is one of the sources for producing such zeta functions. In particular, so called parabolic type PV has rich mathematical structures, and is regarded as important for a number of research areas, including number theory. Currently, I am working on those parabolic type PVs, with applications to number theory, and finding relations to related research areas.

Primary Publications :
  1. Takashi Taniguchi and Frank Thorne, Secondary terms in counting functions for cubic fields, Duke Math. J. 162 (2013), 2451-2508.
  2. Yasuo Ohno, Takashi Taniguchi and Satoshi Wakatsuki, Relations among Dirichlet series whose coefficients are class numbers of binary cubic forms, Amer. J. Math. 131-6 (2009), 1525-1541.
  3. Takashi Taniguchi, A mean value theorem for the square of class number times regulator of quadratic extensions, Ann. Inst. Fourier. 58-2(2008), 625-670.
  4. Takashi Taniguchi, On proportional constants of the mean value of class numbers of quadratic extensions, Trans. Amer. Math. Soc., 359-11(2007), 5517-5524.
  5. Takashi Taniguchi, On the zeta functions of prehomogeneous vector spaces for a pair of simple algebras, Ann. Inst. Fourier. 57-4(2007), 1331-1358.