A database for exponents frequently occurring in analytic number theory

In this talk we will introduce the ANTEDB, an ongoing project that aims to collect and systematize relationships between certain results in analytic number theory, such as exponential sum bounds, zero density estimates and large value theorems. Such results sometimes depend on each other in non-trivial ways, making it difficult to know how combine them most efficiently. In addition, it can be difficult to hypothesize the necessary strength of an intermediary result required to achieve a target bound on a downstream exponent. In this project we develop a set of computational tools to abstract-away the task of optimizing an exponent bound by codifying known relationships between exponents and systematically searching through them. In addition, the database maintains an up-to-date representation of the literature so researchers can quickly compare and combine previously known theorems with new ones.
To demonstrate the usage of the ANTEDB, we apply the optimization routine to a subset of existing literature exponent bounds, systematically obtaining new exponent pairs, zero density estimates, and zero density energy estimates without using any new analytic number theoretic inputs.
This project is joint work with Terence Tao and Tim Trudgian. The code repository for the project is available at https://github.com/teorth/expdb, and a version of the database written in natural language can be found at https://teorth.github.io/expdb/blueprint/.