Three term rational function progressions in finite fields

Autor:	Hong, Guo-Dong, Lim, Zi Li
Rok vydání:	2024
Předmět:	Mathematics - Number Theory Mathematics - Algebraic Geometry Mathematics - Classical Analysis and ODEs Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	Let $F(t),G(t)\in \mathbb{Q}(t)$ be rational functions such that $F(t),G(t)$ and the constant function $1$ are linearly independent over $\mathbb{Q}$, we prove an asymptotic formula for the number of the three term rational function progressions of the form $x,x+F(y),x+G(y)$ in subsets of $\mathbb{F}_p$. The main new ingredient is an algebraic geometry version of PET induction that bypasses Weyl's differencing. This answers a question of Bourgain and Chang. Comment: 17 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2401.01137 Zobrazit plný text záznamu View this record from Arxiv