Exotic Poisson summation formulas on the real line

A crystalline measure is a measure whose support is a discrete closed set,
and whose Fourier transform is also a measure with this property. A
generalized Dirac comb is always crystalline, and all other crystalline
measures are called exotic. I will describe a recent construction of a
continuous family of exotic crystalline measures that uses weakly
holomorphic modular forms on the Hecke group.
The talk is based on a joint work with Maryna Viazovska.