Muhammad Ammar | Searcharxiv

arXiv2026

Quaternionic Nevanlinna Functions

Nevanlinna theory studies the value distribution of meromorphic functions and provides powerful results in the form of the First and Second Main Theorems. In this paper, we introduce quaternionic analogues of the Nevanlinna functions. Starting from the Jensen formula due to Perotti (arXiv:1902.06485), we derive a notion of total order and an associated integrated counting function. We further define quaternionic Weil functions and corresponding mean proximity functions. In this context, we introduce the class of mean proximity balanced functions, which includes the slice-preserving functions and all semiregular functions with a dominating index in their power series. To address the failure of $\log|f^s|$ to be harmonic, we define a Harmonic Remainder Function that compensates for this defect in the Jensen formula. We then prove a weak First Main Theorem--type result for general semiregular functions and obtain a full First Main Theorem for the mean proximity balanced functions.

math.CV↗

arXiv2025

AI-Generated Text Detection in Low-Resource Languages: A Case Study on Urdu

Large Language Models (LLMs) are now capable of generating text that closely resembles human writing, making them powerful tools for content creation, but this growing ability has also made it harder to tell whether a piece of text was written by a human or by a machine. This challenge becomes even more serious for languages like Urdu, where there are very few tools available to detect AI-generated text. To address this gap, we propose a novel AI-generated text detection framework tailored for the Urdu language. A balanced dataset comprising 1,800 humans authored, and 1,800 AI generated texts, sourced from models such as Gemini, GPT-4o-mini, and Kimi AI was developed. Detailed linguistic and statistical analysis was conducted, focusing on features such as character and word counts, vocabulary richness (Type Token Ratio), and N-gram patterns, with significance evaluated through t-tests and MannWhitney U tests. Three state-of-the-art multilingual transformer models such as mdeberta-v3-base, distilbert-base-multilingualcased, and xlm-roberta-base were fine-tuned on this dataset. The mDeBERTa-v3-base achieved the highest performance, with an F1-score 91.29 and accuracy of 91.26% on the test set. This research advances efforts in contesting misinformation and academic misconduct in Urdu-speaking communities and contributes to the broader development of NLP tools for low resource languages.

cs.CL↗