Erdős Type Problems in Modules over Cyclic Rings

2014/06/25 by Yazici, Esen Aksoy
#Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1406.6485

Abstract

In the present paper, we study various Erdős type geometric problems in the setting of the integers modulo q, where q=p^l is an odd prime power. More precisely, we prove certain results about the distribution of triangles and triangle areas among the points of E⊂ ℤ_q². We also prove a dot product result for d-fold product subsets E=A× … × A of ℤ_q^d, where A⊂ ℤ_q.

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