Takashi TANIGUCHI

Takashi TANIGUCHI

Department of Mathematics,
Graduate School of Science, Kobe University
Division : Algebra
Professor		 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. A. Shankar and T. Taniguchi, Secondary terms in the first moment of |Sel2(E)|, Camb. J. Math., 13 (2025), 887-962.
  2. M. Bhargava, T. Taniguchi and F. Thorne, Improved error estimates for the Davenport-Heilbronn theorems, Math. Ann., 389 (2024), 3471-3512.
  3. M. Bhargava, A. Shankar, T. Taniguchi, F. Thorne, J. Tsimerman, and Y. Zhao, Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves, J. Amer. Math. Soc.,33 (2020), 1087-1099.
  4. T. Taniguchi and F. Thorne, Levels of distribution for sieve problems in prehomogeneous vector spaces, Math. Ann., 376 (2020), 1537-1559.
  5. T. Taniguchi and F. Thorne, Orbital exponential sums for prehomogeneous vector spaces, Amer. J. Math. 142 (2020), 177-213.
  6. T. Taniguchi and F. Thorne, Secondary terms in counting functions for cubic fields, Duke Math. J. 162 (2013), 2451-2508.