Likun Xie

collaborators

5 papers

math.AC2026

On an Instance of the Small Cohen-Macaulay Conjecture II

Likun Xie

We show that any $d$ -dimensional local ring $A$ with a dualizing complex, $depth A = d - 1$ , and cyclic deficiency module $K^{d - 1} (A)$ admits a maximal Cohen--Macaulay module.…

math.NT2026

Products of prime ideals in ray class groups

Likun Xie

We prove that every class in the narrow ray class group modulo an integral ideal $q$ of a fixed number field is represented by a product of three prime ideals of norm at…

math.NT2026

An Arithmetic Sum Associated with the Classical Theta Function

Bruce C. Berndt, Raghavendra N. Bhat, Jeffrey L. Meyer +2

The sum $S (h, k) := \sum_{j = 1}^{k - 1} (- 1)^{j + 1 + [hj / k]}$ appears in the modular transformation formulae of the classical theta function $ϑ_{3} (z)$ . The double sum $S(k) := \sum_{h…

math.NT2025

On a Conjecture of ErdÅs over Function Fields

Likun Xie

Using Katz's equidistribution framework, we show that for any squarefree polynomial $f \in F_{q} [t]$ of degree $n \geq 2$ , every residue class modulo $f$ can be represented a…

math.NT2025

Identities for the product of Two Dirichlet Series Satisfying Hecke's Functional Equation

Bruce C. Berndt, Likun Xie

We derive a general formula for the product of two Dirichlet series that satisfy Hecke's functional equation. Several examples are provided to demonstrate the applicability of the…

On an Instance of the Small Cohen-Macaulay Conjecture II

Products of prime ideals in ray class groups

An Arithmetic Sum Associated with the Classical Theta Function

On a Conjecture of ErdÅs over Function Fields

Identities for the product of Two Dirichlet Series Satisfying Hecke's Functional Equation

On a Conjecture of ErdÅs over Function Fields