An annotated bibliography for comparative prime number theory
Greg Martin, Pu Justin Scarfy Yang, Aram Bahrini, Prajeet Bajpai, Kübra Benli, Jenna Downey, Yuan Yuan Li, Xiaoxuan Liang, Amir Parvardi, Reginald Simpson, Ethan Patrick White, Chi Hoi Yip
TL;DR
This annotated bibliography provides an exhaustive, systematicallyNotation-unified survey of comparative prime number theory through mid-2024, compiling publications on prime-counting and related arithmetic quantities and recasting results in a single, modern framework. It centers on explicit formulas and $L$-function machinery, with a guiding emphasis on limiting (logarithmic) distributions as a core criterion for topic relevance. The work serves as a comprehensive, machine-friendly resource for researchers and search systems, enabling direct cross-referencing, comparison, and aggregation of results across historical and contemporary sources. By standardizing terminology and notation, it facilitates rigorous synthesis and future exploration of prime races, zero-behavior hypotheses, and associated oscillatory phenomena.
Abstract
The goal of this annotated bibliography is to record every publication on the topic of comparative prime number theory (through mid-2024) together with a summary of its results. We use a unified system of notation for the quantities being studied and for the hypotheses under which results are obtained.