This $126,180 National Science Foundation Project Grant, awarded on July 1, 2024 through the Mathematical and Physical Sciences (CFDA #47.049) program, supports research at the University of Mississippi on the properties of L-functions and their connections to classical problems in number theory. The project aims to use tools from Fourier analysis, zeros of L-functions, and modular forms to investigate topics such as bounding the least quadratic non-residue modulo a prime, the least prime in an arithmetic progression, and the behavior of L-function central values. The research also explores applications of L-functions to additive combinatorics. In addition to the primary research activities, the grant provides research training opportunities for graduate students at the University of Mississippi.