Research Lines

The project started with two research lines, and expanded to the following five research lines:

Zeta and L-functions holomorphic and PDE Flows

We propose a detailed study of the PDE Zeta (PDZ) flows, starting by well-posedness and blow up issues. Special solutions will be studied. Finally, our main research problem will be to understand the intersection between the PDZ local solutions (such as zeroes of the Riemann zeta function) and the the behavior of L-functions.

Main members: Castillo, Freire, Muñoz, Martínez, Poblete and Salinas

High Energy Physics and Zeta functions

The Riemann Zeta function has important applications in High Energy Physics (HEP). We will describe new properties of L-functions in HEP to describe essential correlation functions.

Members: Bianchi and Muñoz

Collatz motivated PDE/ODE Flows

We shall introduce the (dispersionless, periodic in space) Collatz flow by using the Collatz operator as the nonlocal operator acting on the Fourier side. Our motivation comes from the Szego operator (Gérard and Grellier). 

Members: Alegría, Poblete, Morales and Muñoz

L-functions and Evolution of de Bruijn zeros

Theoretical and numerical work will be done to understand the evolution of complex-valued heat solutions in the case of L-functions. 

Members: Freire, González-Riquelme, Poblete, Salinas and Muñoz

Retarded and delay ODEs appearing in Number Theory

Asymptotic functions appearing in the description of prime number theorems obey suitable ordinary differential equations. In this research line we shall establish precise asymptotic formulae for the long time behavior of these special functions.

Members: Alegría, Carrasco, Poblete and Pozo