Year of Graduation


Level of Access

Open Access Thesis

Embargo Period


Department or Program


First Advisor

Naomi Tanabe


We begin with the classical study of the Riemann zeta function and Dirichlet L-functions. This includes a full exposition on one of the most useful ways of exploiting their connection with primes, namely, explicit formulae. We then proceed to introduce statistics of low-lying zeros of Dirichlet L-functions, discussing prior results of Fiorilli and Miller (2015) on the 1-level density of Dirichlet L-functions and their achievement in surpassing the prediction of the powerful Ratios Conjecture. Finally, we present our original work partially generalizing these results to the case of Hecke L-functions over imaginary quadratic fields.

Included in

Number Theory Commons