Arithmetic, L-functions, and Pseudorandomness

The proposed workshop focuses on recent breakthroughs in arithmetic functions, L-functions, and pseudorandomness in Number Theory, as well as new connections to other areas (via both employed methods and applications), such as additive combinatorics, arithmetic statistics, and dynamical systems. Such breakthroughs include the latest advances in the study of various character and exponential sums (e.g., Kloosterman sums), which are powerful and versatile tools for understanding the anatomy of integers; moments, and other averages of L -functions (over number fields and function fields); integers having a prescribed arithmetic structure (e.g., prime, smooth, square-free, sum of two squares), along with their distribution in arithmetic progressions and short intervals, as well as function field analogs of these problems; distribution of elements of multiplicative subgroups; pseudorandomness of arithmetical functions. An essential aspect of these developments is the vast arsenal of tools and techniques that have been conceived, developed, and implemented, ranging from analysis to additive combinatorics, algebraic geometry, and random matrix theory. The proposed workshop will concentrate on the emerging methods that underlie such advances and on possible future directions.