64 citations · 114 across the 16 of their papers we have counts for
16 papers
Improved error estimates for the Davenport-Heilbronn theorems
Manjul Bhargava, Takashi Taniguchi, Frank Thorne
We improve the error terms in the Davenport-Heilbronn theorems on counting cubic fields to . This improves on separate and independent results of the authors and Sh…
The local-global property for bitangents of plane quartics
Yasuhiro Ishitsuka, Tetsushi Ito, Tatsuya Ohshita +2
We study the arithmetic of bitangents of smooth quartics over global fields. With the aid of computer algebra systems and using Elsenhans--Jahnel's results on the inverse Galois pr…
Uniform bounds for lattice point counting and partial sums of zeta functions
David Lowry-Duda, Takashi Taniguchi, Frank Thorne
We prove uniform versions of two classical results in analytic number theory. The first is an asymptotic for the number of points of a complete lattice in…
Levels of distribution for sieve problems in prehomogeneous vector spaces
Takashi Taniguchi, Frank Thorne
In a companion paper, we developed an efficient algebraic method for computing the Fourier transforms of certain functions defined on prehomogeneous vector spaces over finite field…
Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves
Manjul Bhargava, Arul Shankar, Takashi Taniguchi +3
We prove the first known nontrivial bounds on the sizes of the 2-torsion subgroups of the class groups of cubic and higher degree number fields (the trivial bound being $O_ε(|{…
Orbital exponential sums for prehomogeneous vector spaces
Takashi Taniguchi, Frank Thorne
Let (G, V) be a prehomogeneous vector space, let O be any G(F_q)-invariant subset of V(F_q), and let f be the characteristic function of O. In this paper we develop a method for ex…