Euler Products for Dirichlet L-Functions in the Critical Strip by Tate Chutkow '25

We study the behavior of Euler products associated with Dirichlet $L$-functions within the critical strip. We begin by specializing and adapting the work of Keith Conrad to the setting of Dirichlet $L$-functions, establishing a connection between the asymptotic behavior of partial Euler products and the Riemann hypothesis. In the second half of the paper, we present computational evidence supporting this connection, analyzing the convergence of partial products along the critical line and their behavior near nontrivial zeros. We further develop a representation of Euler products as smooth number series, giving insight into how rearrangements of Dirichlet series affect convergence on the critical line.