In this article, we prove a general theorem which establishes the existence of limiting
distributions for a wide class of error terms from prime number theory. As a corollary to our …

Under the assumption of the Riemann hypothesis, the Linear Independence hypothesis, and
a bound on negative discrete moments of the Riemann zeta function, we prove the existence …

This is a list of problems that were collected from participants at the Comparative Prime
Number Theory Symposium held at UBC from June 17 to June 21, 2024. Its goal is to …

We study the inequities in the distribution of Frobenius elements in Galois extensions of the
rational numbers with Galois groups that are either dihedral D 2 n or (generalized) …

For any k≥ 1, we study the distribution of the difference between the number of integers n≤
x with ω (n)= k or Ω (n)= k in two different arithmetic progressions, where ω (n) is the number …

We investigate the race between prime numbers in many residue classes modulo q,
assuming the standard conjectures GRH and LI. Among our results we exhibit, for the first …

We continue to investigate the race between prime numbers in many residue classes
modulo q, assuming the standard conjectures GRH and LI. We show that provided n/\log q …

Using the same heuristic argument leading to the Lang-Waldschmidt Conjecture in the
theory of linear forms in logarithms, we formulate an effective version of the Linear …

Hooley conjectured that the variance V (x; q) of the distribution of primes up to x in the
arithmetic progressions modulo q is asymptotically, in some unspecified range of q≤ x. On …

Fix a prime p> 2 p>2 and a finite field F q F_q with q elements, where q is a power of p. Let m
be a monic polynomial in the polynomial ring F q T F_qT such that deg (m) \deg(m) is large …