6 citations · 14 across the 12 of their papers we have counts for
14 papers
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.…
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…
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…
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…
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…
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…
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…
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_{…
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…
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…
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…
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…
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…
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…