Showing math.NTShow all
3 papers · 1 filter
math.NT2025
The distribution of prime values of random polynomials
Noah Kravitz, Katharine Woo, Max Wenqiang Xu
The Bateman--Horn Conjecture predicts how often an irreducible polynomial assumes prime values. We demonstrate that with sufficient averaging in the coeffi…
math.NT2025
A random polynomial with multiplicative coefficients is almost surely irreducible
Péter P. Varjú, Max Wenqiang Xu
Assume that the Riemann hypothesis holds for Dedekind zeta functions. Under this assumption, we prove that a degree polynomial with random multiplicative coefficients is…
math.NT2024
Oscillations of random multiplicative functions under initial bias
Rodrigo Angelo, Max Wenqiang Xu
We prove that if is a random completely multiplicative function, conditional for each prime , the probability that …