# Bound on asymptotics of magnitude of three point coefficients in 2D CFT

## TL;DR

This paper rigorously analyzes the asymptotic behavior of heavy-light-heavy three point coefficients in 2D CFTs using complex Tauberian methods, deriving bounds and verifying them numerically.

## Contribution

It introduces a rigorous approach to understanding the asymptotics of three point coefficients in 2D CFTs, including bounds and averaging conditions.

## Key findings

- Derived bounds for average heavy-light-heavy three point coefficients
- Identified conditions for exponential suppression of coefficients
- Numerically verified the theoretical bounds

## Abstract

We use methods inspired from complex Tauberian theorems to make progress in understanding the asymptotic behavior of the magnitude of heavy-light-heavy three point coefficients rigorously. The conditions and the precise sense of averaging, which can lead to exponential suppression of such coefficients are investigated. We derive various bounds for the typical average value of the magnitude of heavy-light-heavy three point coefficients and verify them numerically.