1 citations · 1 across the 10 of their papers we have counts for
11 papers
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…
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_{…
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…
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}:\m…
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.
Generation of Random (Generalized) Orthogonal Matrices
Ali Saraeb
This paper presents an algorithmic method for generating random orthogonal matrices \(A\) that satisfy the property \(A^t S A = S\), where \(S\) is a fixed real invertible symmetri…
On the Generalization of Radamacher's Proof to
Ali Saraeb, Maher Me'meh
In this paper, we generalize Rademacher's proof of the transformation law of the eta function to the Jacobi theta function using Residue calculus.
A generalization of Iseki Formula and the transformation of
Maher Me'meh, Ali Saraeb
In this paper we give a generalization of Iseki's formula and use it to prove the transformation law of .
Generalization of Siegel's Method to theta 1
Maher Me'meh, Ali Saraeb
We present a new proof of the transformation law of under the action of the generator of the full modular group using Siegel's method.
A New Proof For The Transformation Laws of Theta Functions
Maher Me'meh, Ali Saraeb
We prove the transformation laws of the four Jacobi theta functions using Gordon's proof for the transformation law of the Dedekind eta function.