Analytic Number Theory Exponent Database

The Analytic Number Theory Exponent Database (ANTEDB) is an ongoing project to systematically record known theorems for various exponents appearing in analytic number theory, as well as the relationships between them. Currently, the database is recording facts and conjectures on exponent pairs, exponential sum bounds, zero-density and moment bounds for the Riemann zeta-function, large value estimates, additive energy bounds and exponents related to prime distributions, amongst other results. The database aims to organise and record theorems and relationships as both human-readable proofs and as executable python code.

解析数论指数数据库（Analytic Number Theory Exponent Database, ANTEDB）是一项持续性系统性收录项目，旨在系统化记录解析数论领域各类出现的指数相关已知定理，以及各指数间的内在关联关系。目前，该数据库正收录指数对、指数和界、黎曼ζ函数（Riemann zeta-function）的零点密度与矩界、大值估计、加性能量界，以及与素数分布相关的指数等各类研究结论与猜想，同时涵盖其他相关研究成果。本数据库旨在将各类定理及其关联关系，以人类可读的证明形式与可执行Python代码两种形式进行组织与留存。

搜集汇总

背景与挑战

背景概述

该数据集是一个持续更新的项目，旨在系统记录解析数论中各类指数相关的已知定理、猜想及其相互关系，涵盖指数对、指数和界、黎曼ζ函数零密度估计等多个主题。它以人类可读的证明和可执行Python代码形式组织数据，支持社区贡献和动态维护。