Number Theory Seminar: David Roberts

We summarize the theory of Plancherel measures for real groups in a way which makes direct connections with L-functions through their gamma factors. These measures give a "first guess" as to how many L-functions there should be with certain numerical invariants. We compare the theory with L-functions which are currently on the LMFDB and discuss places where the Plancherel theory suggests to look for more L-functions with small conductor.