Abstract: The study of the Riemann Zeta function is of utmost importance, particularly for the connection with the distribution of prime numbers and the Riemann Hypothesis. This work presents a different approach by addressing this problem in Number Theory using techniques from partial differential equations (PDEs). To establish this connection, we examine a heat equation with the Riemann Zeta function as the source term.

On this occasion, our focus will be on the two main theorems we have proven. Firstly, we will discuss the theorem on local existence of solutions for small time intervals, and its extension to a family of functions including Zeta, the Dirichlet L-functions. Additionally, we will provide conditions to ensure the global existence and the asymptotic behavior of the flow.

Venue: DIM seminar room, Beauchef 851, 5th floor.