Number Theory Seminar

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).