8 citations · 17 across the 12 of their papers we have counts for
13 papers
On the generalization of Christol's theorem to domains of finite type over finite fields
Lian Duan, Chunlin Wang
We generalize Christol's theorem---which characterizes algebraic power series over a finite field in terms of automatic coefficient sequences---to completions of domains of finite…
A geometric approach to the density of rank-metric codes
Shamil Asgarli, Lian Duan, Nathan Kaplan +1
We study the asymptotic density of -point-free linear sections of geometrically irreducible projective varieties over finite fields. We then apply these results to ra…
Galois representation of the product of two Drinfeld modules of generic characteristic
Lian Duan, Jiangxue Fang
In this paper, we study the Galois representations attached to products of Drinfeld modules. As a function-field analogue of Serre's classical open image theorem for products of el…
On the essential torsion finiteness of abelian varieties over torsion fields
Jeff Achter, Lian Duan, Xiyuan Wang
The classical Mordell-Weil theorem implies that an abelian variety over a number field has only finitely many -rational torsion points. This finitude of torsion still ho…
Frobenius nonclassical hypersurfaces
Shamil Asgarli, Lian Duan, Kuan-Wen Lai
A smooth hypersurface over a finite field is called Frobenius nonclassical if the image of every geometric point under the -th Frobenius endomorphism remains in t…
Nonsplitting of the Hilbert exact sequence and the principal Chebotarev density theorem
Lian Duan, Kelly Emmrich, Ning Ma +1
Let be a finite Galois extension of number fields, and let be the Hilbert class field of . We find a way to verify the nonsplitting of the short exact sequence $$1\t…
Generalizations of Alladi's formula for arithmetical semigroups
Lian Duan, Ning Ma, Shaoyun Yi
In this article, we prove that a general version of Alladi's formula with Dirichlet convolution holds for arithmetical semigroups satisfying Axiom or Axiom . As applica…
Analogues of Alladi's formula over global function fields
Lian Duan, Biao Wang, Shaoyun Yi
In this paper, we show an analogue of Kural, McDonald and Sah's result on Alladi's formula for global function fields. Explicitly, we show that for a global function field , if…
Transverse linear subspaces to hypersurfaces over finite fields
Shamil Asgarli, Lian Duan, Kuan-Wen Lai
Ballico proved that a smooth projective variety of degree over a finite field of elements admits a smooth hyperplane section if . In this paper,…
Irreducibility of geometric Galois representations and the Tate conjecture for a family of elliptic surfaces
Lian Duan, Xiyuan Wang
Using Calegari's result on the Fontaine-Mazur conjecture, we study the irreducibility of pure, regular, rank 3 weakly compatible systems of self-dual l-adic representations. As a c…
Faltings Serre method on three dimensional selfdual representations
Lian Duan
We prove that a selfdual -Galois representation constructed by van Geemen and Top is isomorphic to a quadratic twist of the symmetric square of the Tate module of an elliptic…
Transverse lines to surfaces over finite fields
Shamil Asgarli, Lian Duan, Kuan-Wen Lai
We prove that if is a smooth reflexive surface in defined over a finite field , then there exists an -line meeting transversely p…
Galois action on the Neron-Severi group of Dwork surfaces
Lian Duan
We study the Galois action attached to the Dwrok surfaces with parameter in a number field . We show that when has geome…