Some Results on Zero Sum Sequences in Z_p³

2014/09/09 by Satwik Mukherjee, Mukherjee, Satwik
Computer Science · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1409.2843

This was a part of my master thesis under Prof. Gautami Bhowmik

arxiv created 2014/09/09 · openalex publication_date 2014/09/09 · arxiv updated 2014/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Kemnitz Conjecture [9] states that if we take a sequence of elements in Z_p² of length 4p-3, p is a prime number, then it has a subsequence of length p, whose sum is 0 modulo p. It is known that in Z_p³ to get a similar result we have to take a sequence of length atleast 9p-8 . In this paper we will show that if we add a condition on the chosen sequence, then we can get a good upper and a lower bound for which similar results hold.

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