Machine Learning for Number Theory: Unsupervised Learning with L-Functions

There is a strong tradition of computation in number theory, with notable data-driven insights including the prime number theorem and the conjecture of Birch and Swinnerton-Dyer. A huge arithmetic online database known as the LMFDB went live in the mid-2010 s, to which we began applying machine learning methodologies in 2020. This led to a data scientific perspective on old problems, and the discovery of surprising new structures in arithmetic statistics known as murmurations. In this extended abstract, we will apply unsupervised learning techniques to a small dataset taken from the LMFDB, chosen so as to demonstrate one approach to generalising the original experiments.