Rademacher Expansions and the Spectrum of 2d CFT

I will describe work exploring the spectrum of two-dimensional unitary conformal field theories(CFT) with no extended chiral algebra and central charge larger than one. I will revisit a classical result from analytic number theory by Rademacher, which provides an exact formula for the Fourier coefficients of modular forms of non-positive weight. Generalizing this, I will explain how we employed Rademacher's idea to study the spectral density of two-dimensional CFT of our interest. The expression is given in terms of a Rademacher expansion, which converges for nonzero spin. The implications of our spectral density to the pure gravity in AdS3 will be discussed.