# Semi-algebraic properties of Minkowski sums of a twisted cubic segment

## TL;DR

This paper provides a semi-algebraic description of Minkowski sums of multiple twisted cubic segments, enabling efficient membership testing and applications to the matrix moment problem related to L-functions.

## Contribution

It introduces a semi-algebraic characterization of Minkowski sums of twisted cubic segments, facilitating computational tests and applications in number theory.

## Key findings

- Semi-algebraic descriptions for Minkowski sums of twisted cubics
- Efficient membership testing algorithms developed
- Applications to the matrix moment problem and L-functions

## Abstract

We find a semi-algebraic description of the Minkowski sum $\mathcal{A}_{3,n}$ of $n$ copies of the bounded twisted cubic $\{(t,t^2,t^3)\mid -1\leq t\leq 1\}$ for each integer $n\geq3$. These descriptions provide efficient membership tests for the sets $\mathcal{A}_{3,n}$. These membership tests in turn can be used to resolve some instances of the underdetermined matrix moment problem, which was formulated by Michael Rubinstein and Peter Sarnak in order to study problems related to $L$-functions and their zeros.