On L-functions and the 1-Level Density

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.

About this item

Creator: Arav Agarwal

Date: 2023-01-01

Contributor: Naomi Tanabe, Advisor

Bowdoin Department or Program: Mathematics

Subject: Number Theory; riemann zeta function; dirichlet L functions; analytic number theory; algebraic number theory; 1-level density; Hecke L-functions; f-ray class L-functions; L-functions; explicit formula; ratios conjecture

Access: Open access

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