Identities for the product of Two Dirichlet Series Satisfying Hecke's Functional Equation
Bruce C. Berndt, Likun Xie
TL;DR
This paper derives a general formula for the product of two Dirichlet series satisfying Hecke's functional equation, with examples and clarifications on related prior work.
Contribution
It introduces a new general formula for such products and addresses issues in existing literature.
Findings
The formula applies to various examples of Dirichlet series.
Clarifies misunderstandings in previous research.
Provides a framework for future studies on Dirichlet series products.
Abstract
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 formula. In addition, we discuss prior work on similar products and clarify certain issues arising in the existing literature.
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Taxonomy
TopicsMeromorphic and Entire Functions · Functional Equations Stability Results · Analytic Number Theory Research