5 papers · 1 filter
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_{…
Unimodular Fake Mobius Functions
Ali Saraeb
Let denote the unit circle. We introduce and develop the analytic and bias theory of unimodular fake Möbius functions, i.e. multiplicative functions $\mathfrak{f}:\…
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…
Computational Experiments in Number Theory
Ali Saraeb
This paper presents two concrete applications of Artificial Intelligence to algorithmic and analytic number theory. Recent benchmarks of large language models have mainly focused o…
Significance of Zeros and Gram Points in Approximating and Discovering Zeros of Dirichlet L-functions
Ali Saraeb
We propose a numerical method for approximating and discovering zeros of the Dirichlet L-function L(s, chi) corresponding to real Dirichlet characters chi.