64 citations · 140 across the 23 of their papers we have counts for
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math.NT2017★ 5 cited
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…
math.NT2017
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…
math.NT2017★ 13 cited
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(|{…