Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the number of dot product chains in finite fields and rings   We explore variants of Erd\H os' unit distance problem concerning dot
products between successive pairs of points chosen from a large finite subset
of either $\mathbb F_q^d$ or $\mathbb Z_q^d,$ where $q$ is a power of an odd
prime. Specifically, given a large finite set of points $E$, and a sequence of
elements of the base field (or ring) $(\alpha_1,\ldots,\alpha_k)$, we give
conditions guaranteeing the expected number of $(k+1)$-tuples of distinct
points $(x_1,\dots, x_{k+1})\in E^{k+1}$ satisfying $x_j \cdot
x_{j+1}=\alpha_j$ for every $1\leq j \leq k$.

14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph