17 citations · 19 across the 9 of their papers we have counts for
9 papers
-invariant on unary Hermitian lattices over imaginary quadratic fields with class number or
Jingbo Liu
In this paper, we study the unary Hermitian lattices over imaginary quadratic fields. Let be an imaginary quadratic field for a square-free positi…
A Note on Affine Invariant Cost Functions
Jingbo Liu
We show that any affine invariant function on the set of positive definite matrices must factor through the determinant function, as long as the restriction of the function to scal…
A new proof of Legendre's theorem on the Diophantine equation
Jingbo Liu, Bruce McOsker
One of Legendre's theorems on the Diophantine equation provides necessary and sufficient conditions on the existence of nonzero rational solutions of this equati…
On the value distribution of the Riemann zeta-function and the Euler gamma-function
Qi Han, Jingbo Liu, Qiong Wang
We prove some uniqueness results for the Riemann zeta-function and the Euler gamma-function by virtue of shared values using the value distribution theory.
On differential independence of $\mathboldζ$ and $\mathboldΓ$
Qi Han, Jingbo Liu
In this note, we will prove that $\mathboldζ$ and $\mathboldΓ$ can not satisfy any differential equation generated through a family of functions continuous in $\mathboldζ$ with pol…
Algebraic differential independence regarding the Riemann -function and the Euler -function
Qi Han, Jingbo Liu
In this paper, we prove that cannot be a solution to any nontrivial algebraic differential equation whose coefficients are polynomials in $\boldsymbolΓ,\boldsymbolΓ^…
Universal sums of -gonal numbers
Ben Kane, Jingbo Liu
In this paper we study universal quadratic polynomials which arise as sums of polygonal numbers. Specifically, we determine an asymptotic upper bound (as a function of ) on the…
On Fermat Diophantine functional equations and little Picard theorem
Jingbo Liu, Qi Han, Wei Chen
We discuss equivalence conditions on the non-existence of non-trivial meromorphic solution to the Fermat Diophantine equations with integers , from whic…
On a Waring's problem for integral quadratic and hermitian forms
Constantin N. Beli, Wai Kiu Chan, Maria Ines Icaza +1
For each positive integer , let be the smallest integer such that if an integral quadratic form in variables can be written as a sum of squares of integra…