Year: 2015
Type: preprint
Abstract: For $B\subset\mathbb{R}^k$ denote by $Φ_k(Q;B)$ the number of ordered $k$-tuples in $B$ of real conjugate algebraic numbers of degree $\leq n$ and naive height $\leq Q$. We show that $$ Φ_k(Q;B) = \frac{(2Q)^{n+1}}{2ζ(n+1)} \int_{B} ρ_k(\mathbf{x})\,d\mathbf{x} + O\left(Q^n\right),\quad Q\to \infty, $$ where the function $ρ_k$ will be given explicitly. If $n=2$, then an additional factor $\log Q$ appears in the reminder term.
Source: arXiv (Cornell University)
Authors: Götze, Friedrich, Kaliada, Dzianis, Zaporozhets, Dmitry
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2190779876