On a Certain Integral Over a Triangle

TL;DR

This paper investigates specific integrals over a triangle with vertices at (1,0), (0,1), and (1,1), demonstrating how they produce linear combinations of multiple zeta values, thus linking geometric integrals to special number theory constants.

Contribution

It introduces a novel analysis of integrals over a particular triangle that relate to multiple zeta values, expanding understanding of their geometric and algebraic connections.

Findings

Integrals over the specified triangle yield linear combinations of multiple zeta values.

The study establishes a new link between geometric integrals and number theory constants.

Results suggest potential applications in understanding the structure of multiple zeta values.

Abstract

We study integrals over the triangle with vertices (1,0), (0,1), (1,1) that give linear combinations of multiple zeta values.