activity
20132026
most citedOn indefinite -universal integral quadratic forms over number fields

6 citations · 14 across the 12 of their papers we have counts for

collaborators

14 papers

math.NT2026

The compositional inverses of the permutation polynomials of the form over

Danyao Wu, Xuan Pang, Zilong He +1

This paper focuses on computing the compositional inverses of permutation polynomials of the form over finite fields via the local method.…

math.NT2023

The mass of shifted lattices and class numbers of inhomogeneous quadratic polynomials

Kathrin Bringmann, Zilong He, Ben Kane

In this paper, we investigate class numbers of shifted quadratic lattices with and odd conductor . For a lattice…

math.NT2022★ 2 cited

On classic -universal quadratic forms over dyadic local fields

Zilong He

Let be an integer and . A classic integral quadratic form over local fields is called classic -universal if it represents all -ary classic integral quadrati…

math.NT2022

Pythagoras number of quartic orders containing

Zilong He, Yong Hu

Let be a quartic number field containing and let be an order such that . We prove that the Pythagoras number of $\m…

math.NT2022★ 3 cited

On -universal quadratic lattices over unramified dyadic local fields

Zilong He, Yong Hu

Let be a positive integer and let be a finite unramified extension of with ring of integers . An integral (resp. classic) quadratic form over…

math.NT2022★ 2 cited

On -universal quadratic forms over dyadic local fields

Zilong He, Yong Hu

Let be an integer. We give necessary and sufficient conditions for an integral quadratic form over dyadic local fields to be -universal by using invariants from Bel…

math.NT2022★ 6 cited

On indefinite -universal integral quadratic forms over number fields

Zilong He, Yong Hu, Fei Xu

An integral quadratic lattice is called indefinite -universal if it represents all integral quadratic lattices of rank for a given positive integer . For , we pr…

math.NT2020

Inequalities for inert primes and their applications

Zilong He

For any given non-square integer , we prove Euclid's type inequalities for the sequence of all primes satisfying the Kronecker symbol $ (D/q_{…

math.NT2020

Sign changes of Fourier coefficients of cusp forms of half-integral weight over split and inert primes in quadratic number fields

Zilong He, Ben Kane

In this paper, we investigate sign changes of Fourier coefficients of half-integral weight cusp forms. In a fixed square class , we investigate the sign changes in t…

math.NT2019

Regular ternary polygonal forms

Zilong He, Ben Kane

Inspired by Dickson's classification of regular ternary quadratic forms, we prove that there are no primitive regular -gonal forms when is sufficiently large. In order to do…

math.NT2015

On the sum of reciprocal generalized Fibonacci numbers

Pingzhi Yuan, Zilong He, Junyi Zhuo

In this paper, we consider infinite sums derived from the reciprocals of the generalized Fibonacci numbers. We obtain some new and interesting identities for the generalized Fibona…

math.CO2014

New result and some open problems on the primitive degree of nonnegative tensors

Pingzhi Yuan, Zilong He, Lihua You

In this paper, we show that the exponent set of nonnegative primitive tensors with order m(\geq 3) and dimension n is {1,2,\ldots, (n-1)^2+1}; and propose some open problems for fu…

math.CO2014★ 1 cited

On the exponent set of nonnegative primitive tensors

Zilong He, Pingzhi Yuan, Lihua You

In this paper, we present a necessary and sufficient condition for a nonnegative tensor to be a primitive one, show that the exponent set of nonnegative primitive tensors with orde…

math.CO2013

A conjecture on the primitive degree of Tensors

Pingzhi Yuany, Zilong He, Lihua You

In this paper, we prove: Let A be a nonnegative primitive tensor with order m and dimension n. Then its primitive degree R(A)\leq (n-1)^2+1, and the upper bound is sharp. This conf…