Non-vanishing for cubic Hecke $L$-functions

Series
Athens-Atlanta Number Theory Seminar
Time
Tuesday, October 28, 2025 - 4:00pm for 1 hour (actually 50 minutes)
Location
Emory, Mathematics and Science Center, W303
Speaker
Alexander Dunn – Georgia Tech – adunn61@gatech.eduhttps://alexjdunn.weebly.com/
Organizer
Raman Parimala

In this talk I will discuss a recent result that establishes an unconditional proportion of non-vanishing at the central point $s=1/2$ for cubic Hecke $L$-functions over the Eisenstein quadratic number field. This result comes almost 25 years after Soundararajan’s (2000) breakthrough result for the positive proportion of non-vanishing for primitive quadratic Dirichlet $L$-functions over the rational numbers.

In this talk I will explain why number theorists care about non-vanishing for $L$-functions, and why the non-vanishing problem for cubic L-functions has starkly different features to the quadratic case. This is a joint work with A. De Faveri (Stanford), C. David (Concordia), and J. Stucky (Georgia Tech).