An annotated bibliography for comparative prime number theory

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.

110 pages; supersedes "Comparative prime number theory: A survey" (arXiv:1202.3408). Accepted (Dec. 2024) for publication in Expositiones Mathematicae

References in corpus (10)

• The large sieve, monodromy and zeta functions of algebraic curves, II: independence of the zeros
• Application of an accurate remainder term in the calculation of Residue Class Distributions
• Sign changes of $\pi (x,q,1)-\pi (x,q,a)$
• A New Aspect of Chebyshev's Bias for Elliptic Curves over Function Fields
• Lower bounds for negative moments of ${\zeta }^{\prime }(\rho )$
• Exceptional biases in counting primes over functions fields
• Prime Running Functions
• Euler Products at the Centre and Applications to Chebyshev's Bias
• Comparative Prime Number Theory Problem List
• Sign changes in Mertens' first and second theorems

Cited by in corpus (1)

• Oscillation results for the summatory functions of fake mu's