Likun Xie

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20242026

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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.NT2025

On a Conjecture of Erdős 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

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.NT2024

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…