On the new bound for the number of solutions of polynomial equations in subgroups and the structure of graphs of Markoff triples

2017/11/14 by Sergeĭ Konyagin, Sergey Makarychev, Konyagin, S. V. +5
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1711.05335

openalex publication_date 2017/11/14 · openalex created_date 2017/12/04 · openalex updated_date 2026/07/28

Abstract

We sharpen the bounds of J. Bourgain, A. Gamburd and P. Sarnak (2016) on the possible number of nodes outside the "giant component" and on the size of individual connected components in the suitably defined functional graph of Markoff triples modulo p. This is a step towards the conjecture that there are no such nodes at all.

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