Year: 2025
Type: article
Abstract: A famous conjecture of Chowla on the least primes in arithmetic progressions implies that the abscissa of convergence of the Weil representation zeta function for a procyclic group G only depends on the set S of primes dividing the order of G and that it agrees with the abscissa of the Dedekind zeta function of ℤ [ p - 1 ∣ p ∉ S ] {\mathbb{Z}[p^{-1}\mid p\not\in S]} . Here we show that these consequences hold unconditionally for random procyclic groups in a suitable model. As a corollary, every real number 1 ≤ β ≤ 2 {1\leq\beta\leq 2} is the Weil abscissa of some procyclic group.
Source: Forum Mathematicum
Author: Steffen Kionke
Institution: FernUniversität in Hagen
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4413804901