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math.NT2018
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…
math.NT2018
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…
math.NT2017
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…