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math.NT2026
Resurgent rigidity of mock theta functions: uniqueness and natural boundary crossing
Ovidiu Costin, Gerald V. Dunne, Ali Saraeb
We develop a resurgent transseries approach to mock theta functions and show that the associated Mordell--Appell integrals underlie their modular and resurgent structure. From thes…
math.NT2026
Functional Equations Characterize Dirichlet Characters
Ghaith Hiary, Ali Saraeb
We prove a converse theorem for functional equations of Dirichlet -functions. Under mild assumptions, we prove that these functional equations for -series of the form $\sum_{…
math.NT2026
On Uniqueness of Mock Theta Functions
Ovidiu Costin, Gerald V. Dunne, Ali Saraeb
We develop a resurgent approach to the problem of unique continuation of mock theta functions across their natural boundary. The starting point is the representation of the associa…