Upper and Lower Bounds for Kronecker Constants of Three-Element Sets of Integers

TL;DR

This paper investigates bounds for the angular Kronecker constants of three-element integer sets, providing new bounds, examples where bounds are attained, and conjectures about the minimal upper bounds.

Contribution

It establishes new upper and lower bounds for the Kronecker constants of three-element integer sets and explores cases where these bounds are tight.

Findings

Bounds are attained in specific examples.

5/16 bounds the angular Kronecker constants for positive integer sets.

Numerous examples suggest the minimal upper bound is 1/4.

Abstract

Various upper and lower bounds are provided for the (angular) Kronecker constants of sets of integers. Some examples are provided where the bounds are attained. It is proved that 5=16 bounds the angular Kronecker constants of 3-element sets of positive integers. However, numerous examples suggest that the minimum upper bound is 1=4 for 3-element sets of positive integers.