Linear forms of a given Diophantine type and lattice exponents

TL;DR

This paper proves an existence theorem for linear forms of a specific Diophantine type and explores the structure of the spectrum of lattice exponents, advancing understanding in Diophantine approximation.

Contribution

It introduces a new existence theorem for linear forms of a given Diophantine type and analyzes the spectrum of lattice exponents.

Findings

Existence theorem for linear forms of a given Diophantine type

Structural insights into the spectrum of lattice exponents

Application of the theorem to lattice exponent analysis

Abstract

In this paper we prove an existence theorem concerning linear forms of a given Diophantine type and apply it to study the structure of the spectrum of lattice exponents.