Likun Xie

collaborators

4 papers

math.AC2026

Connectedness in Codimension One and the Non- $S_{2}$ Locus

Likun Xie

We formulate a structural principle for finite $S_{2}$ -objects: coherent $S_{2}$ -sheaves and finitely generated graded $S_{2}$ -modules decompose canonically according to the connected co…

math.NT2025

Primes $p$ such that $p - b$ Has a Large Power Factor and Few Other Prime Divisors

Likun Xie

We prove lower bounds for the number of primes $p \leq N + b$ such that $p - b$ is divisible by $2^{k (N)}$ and has at most $k$ odd prime factors ( $k \geq 2$ ), assuming $2^{k(N)} \leq…

math.NT2025

Almost Prime Orders of Elliptic Curves Over Prime Power Fields

Likun Xie

In 1988, Koblitz conjectured the infinitude of primes p for which |E(F_p)| is prime for elliptic curves E over Q, drawing an analogy with the twin prime conjecture. He also propose…

math.NT2025

Almost primes and primes that are sums of two squares plus 1

Kunjakanan Nath, Likun Xie

In this paper, we obtain a lower bound for the number of primes $p \leq x$ such that $p - 1$ is a sum of two squares and $p + 2$ has a bounded number of prime factors. The proof uses th…

Connectedness in Codimension One and the Non-S2​ Locus

Primes p such that p−b Has a Large Power Factor and Few Other Prime Divisors

Almost Prime Orders of Elliptic Curves Over Prime Power Fields

Almost primes and primes that are sums of two squares plus 1

Connectedness in Codimension One and the Non- $S_{2}$ Locus

Primes $p$ such that $p - b$ Has a Large Power Factor and Few Other Prime Divisors