arXiv subjects

Chang Lv

Publications and source records attributed to Chang Lv.

20 records · Page 2Linked to original sources

arXiv2015

On Orders in Number Fields: Picard Groups, Ring Class Fields and Applications

In this article, we focus on orders in arbitrary number fields, consider their Picard groups and finally obtain ring class fields corresponding to them. The Galois group of the ring class field is isomorphic to the Picard group. As an application, we give criteria of the solvability of the diophantine equation $p=x^2+ny^2$ over a class of imaginary quadratic fields where $p$ is a prime element.

math.NT↗

arXiv2013

Primality Test for Numbers of the Form Ap^n+w

We propose an algorithm determining the primality of numbers $M=Ap^n+w_n$ where $w_n^{p-1}\equiv1\pmod{p^n}$ and $A<p^n$ and give example when $p=7$. $p$ th reciprocity law is involved. The algorithm runs in polynomial time in $\log_2(M)$ for fixed $p$ and $A$.

math.NT↗