The PI will study distribution questions in L-functions and multiplicative functions, which are central subjects in multiplicative number theory. The first known example of L-functions is the Riemann zeta function. Classically, its zeros are connected to the distribution of prime numbers, which have applications to cryptography and modern security systems. There has been extensive research on the properties of L-functions, such as the distribution of their zeros and distribution of their values. However, many deep problems remain unsolved even though good conjectures have been formulated. The PI will explore various distributions in families of L-functions and provide insight into the structures of such families; the novel techniques developed will serve as powerful tools to shed light on other deep questions in the area. Another direction of the project is to explore ubiquitous statistical phenomenon known as Benford's law. This law first appeared as an observation about the first digits of the numbers in data sets. In particular, the leading digits do not exhibit uniform distribution as might be naively expected, but rather, the digit 1 appears the most, followed by 2, 3, and so on until 9. The goal is to give an answer in the context of multiplicative functions to the question "Is checking the first digit theoretically equivalent to checking many digits?" The award will provide opportunities for research training and collaboration for students and postdocs. The PI will