Sums of Fractions and Finiteness of Monodromy

TL;DR

This paper addresses a number theory problem involving sums of fractional parts and uses group theory methods to establish the finiteness of specific monodromy representations.

Contribution

It introduces a novel approach combining elementary number theory and group theory to analyze monodromy finiteness.

Findings

Solved a classical problem on sums of fractional parts.

Proved the finiteness of certain monodromy representations.

Applied elementary methods to a problem in algebraic geometry.

Abstract

We solve an elementary number theory problem on sums of fractional parts, using methods from group theory. We apply our result to deduce the finiteness of certain monodromy representations.