Year: 2026
Type: preprint
Abstract: For a fixed integer $n\ge 2,$ we consider the homogeneous polynomial $$ P(x_1, x_2, \ldots, x_{n+2})=\sum_{i=1}^{n} (x_2-x_1)^{i-1} x_1^{n-i} x_{i+2}. $$ We prove that, for any finite set $A$ of complex numbers, $$ \Bigl|\bigl\{P(x_1,x_2,\ldots,x_{n+2}): \, x_i\in A\bigr\}\Bigr|\gg |A|^{n}. $$ The implicit constant in $\gg$ may depend only on $n.$
Source: arXiv (Cornell University)
Authors: Garaev, M. Z., Konyagin, S. V.
Institution: Universidad Nacional Autónoma de México
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G597338630, G6444257319, G6509858906
OpenAlex ID: W7204576656
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