# Amplitudes and the Riemann Zeta Function

### APA

Remmen, G. (2021). Amplitudes and the Riemann Zeta Function . Perimeter Institute. https://pirsa.org/21100004

### MLA

Remmen, Grant. Amplitudes and the Riemann Zeta Function . Perimeter Institute, Oct. 05, 2021, https://pirsa.org/21100004

### BibTex

@misc{ pirsa_21100004, doi = {10.48660/21100004}, url = {https://pirsa.org/21100004}, author = {Remmen, Grant}, keywords = {Quantum Fields and Strings}, language = {en}, title = {Amplitudes and the Riemann Zeta Function }, publisher = {Perimeter Institute}, year = {2021}, month = {oct}, note = {PIRSA:21100004 see, \url{https://pirsa.org}} }

Grant Remmen Kavli Institute for Theoretical Physics (KITP)

## Abstract

In this talk, I will connect physical properties of scattering amplitudes to the Riemann zeta function. Specifically, I will construct a closed-form amplitude, describing the tree-level exchange of a tower with masses m^2_n = \mu^2_n, where \zeta(\frac{1}{2}\pm i \mu_n) = 0. Requiring real masses corresponds to the Riemann hypothesis, locality of the amplitude to meromorphicity of the zeta function, and universal coupling between massive and massless states to simplicity of the zeros of \zeta. Unitarity bounds from dispersion relations for the forward amplitude translate to positivity of the odd moments of the sequence of 1/\mu^2_n.