Machine Learning L-functions - Analyzing Complex Functions in Number Theory

Watch a 33-minute mathematics lecture from Harvard CMSA's Mathematics and Machine Learning Closing Workshop where MIT's Edgar Costa explores the application of machine learning techniques to L-functions data analysis. Delve into research examining two distinct L-function datasets: one containing approximately 250,000 rational L-functions of small arithmetic complexity from various origins, and another comprising L-functions associated with Maass forms. Learn how different dimensionality reduction techniques were employed to analyze invariants and behavioral patterns, with particular attention to the impact of varying origins on results. Discover a proposed heuristic method for deducing the Fricke sign, an unknown invariant for 40% of Maass form L-functions data. Gain insights into how L-functions encode crucial information about number theory and algebraic geometry, and their significance in the Langlands program, which connects number theory with other mathematical domains.