Yongqiang Zhao

activity

20172024

most citedBounds on 2-torsion in class groups of number fields and integral points on elliptic curves

13 citations · 14 across the 6 of their papers we have counts for

collaborators

8 papers

math.SP2024

On the multiplicity of the eigenvalues of discrete tori

Bing Xie, Yigeng Zhao, Yongqiang Zhao

It is well known that the standard flat torus $T^{2} = R^{2} / Z^{2}$ has arbitrarily large Laplacian-eigenvalue multiplicities. We prove, however, that $24$ is the optima…

math.AG2023

Scrollar invariants, syzygies and representations of the symmetric group II

Floris Vermeulen

Let $φ : C \to P^{1}$ be a degree $d$ cover of curves. In work by Castryck, Zhao and the author, we showed how one can attach to each partition $λ$ of $d$ a multi-set of scrol…

math.NT2022

Special values of spectral zeta functions of graphs and Dirichlet L-functions

Bing Xie, Yigeng Zhao, Yongqiang Zhao

In this paper, we establish relations between special values of Dirichlet $L$ -functions and that of spectral zeta functions or $L$ -functions of cycle graphs. In fact, they determin…

math.AG2022

Scrollar invariants, syzygies and representations of the symmetric group

Wouter Castryck, Floris Vermeulen, Yongqiang Zhao

We give an explicit minimal graded free resolution, in terms of representations of the symmetric group $S_{d}$ , of a Galois-theoretic configuration of $d$ points in $\mathbb{P}^{d-2}…

math.NT2018

On a senary quartic form

Jianya Liu, Jie Wu, Yongqiang Zhao

We count rational points of bounded height on the non-normal senary quartic hypersurface x 4 = (y 2 1 + $\times$ $\times$ $\times$ + y 2 4)z 2 in the spirit of Manin's conjecture.

math.NT2017★ 1 cited

On a certain non-split cubic surface

Régis de la Bretèche, Kevin Destagnol, Jianya Liu +2

In this note, we establish an asymptotic formula for the number of rational points of bounded height on the singular cubic surface $x_{0} (x_{1}^{2} + x_{2}^{2}) = x_{3}^{3}$ with a power-savin…

math.NT2017

Manin's conjecture for a class of singular cubic hypersurfaces

Jianya Liu, Jie Wu, Yongqiang Zhao

Let $n$ be a positive multiple of $4$ . We establish an asymptotic formula for the number of rational points of bounded height on singular cubic hypersurfaces $S_{n}$ defined by $$ x^…

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 $K$ (the trivial bound being $O_ε(|{…