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 (32)

• Unexpected biases in the distribution of consecutive primes
• The Distribution of Weighted Sums of the Liouville Function and Pólya's Conjecture
• Chebyshev's bias for analytic L-functions
• Highly biased prime number races
• Lattice algorithms for multivariate approximation in periodic spaces with general weight parameters
• Big biases amongst products of two primes
• The large sieve, monodromy and zeta functions of algebraic curves, II: independence of the zeros
• Lower bounds for discrete negative moments of the Riemann zeta function
• Chebyshev's bias for products of irreducible polynomials
• A note on a conjecture of Gonek
• Distribution of Frobenius elements in families of Galois extensions
• Chebyshev's bias for products of $k$ primes
• Large bias for integers with prime factors in arithmetic progressions
• Limiting properties of the distribution of primes in an arbitrarily large number of residue classes
• A New Aspect of Chebyshev's Bias for Elliptic Curves over Function Fields
• On the Mertens Conjecture for Function Fields
• Application of an accurate remainder term in the calculation of Residue Class Distributions
• Primes in prime number races
• Character sums over products of prime polynomials
• Sign changes of $\pi (x,q,1)-\pi (x,q,a)$
• Sums of two squares are strongly biased towards quadratic residues
• Lower bounds for negative moments of ${\zeta }^{\prime }(\rho )$
• Biases in prime factorizations and Liouville functions for arithmetic progressions
• On the first sign change in Mertens' Theorem
• Prime Running Functions
• Exceptional biases in counting primes over functions fields
• On a Mertens-type conjecture for number fields
• Sign changes in Mertens' first and second theorems
• On the Mertens Conjecture for Elliptic Curves over Finite Fields
• Densities in certain three-way prime number races
• Euler Products at the Centre and Applications to Chebyshev's Bias
• Comparative Prime Number Theory Problem List

Cited by in corpus (2)

• Oscillation results for the summatory functions of fake mu's
• Discrepancies in the distribution of Gaussian primes