Differentiating L-functions

The Riemann zeta function is well known due to its link to prime numbers. The Riemann Xi function is related to the zeta function, and is commonly used due to its nicer analytic properties (such as its lack of a pole and its Fourier transform).

The work within this thesis was inspired by Haseo Ki's result, which showed that, under repeated differentiation and suitable scaling, the Riemann Xi function tends to the cosine function.

We prove a similar result for the Selberg Class of L-functions, albeit with different scalings.