Likun Xie

activity

20242026

collaborators

2 papers

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…