3 papers
math.NT2022
Parametric Euler Sums of Harmonic Numbers
Junjie Quan, Xiyu Wang, Xiaoxue Wei +1
We define a parametric variant of generalized Euler sums and construct contour integration to give some explicit evaluations of these parametric Euler sums. In particular, we estab…
math.NT2021
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…
math.NT2020
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…