Simplicity criteria for zeros of Mittag–Leffler functions
Abstract
In this short work, we establish the necessary and sufficient condition for the simplicity of the zeros of the Mittag–Leffler functions Eα,ζ(z), where α,ζ∈R+. Specifically, we construct a particular class of fractional-order compact integral operators A, such that the zero λ of Eα,ζ(z) corresponds to the eigenvalue 1λ of A. We then demonstrate that the zero λ is simple (or prime) if and only if the algebraic multiplicity of the eigenvalue 1λ is equal to 1 (that is, A has no generalised eigenfunction).
Fields of Study & Subjects
Analytic and geometric function theory
Functional Equations Stability Results
Holomorphic and Operator Theory
Publication details
- Journal / source
- Integral Transforms and Special Functions
- Pages
- 1–13
- Publication date
- 7 January 2026
- Language
- EN