The Z-module of multiple zeta values is generated by ones for indices without ones

Key Points

• This work aims to show that every multiple zeta value can be generated as a linear combination of a specific type of zeta value.
• Introduced modified multiple harmonic sums
• Established relations among multiple zeta values
• Determined the structure of the generated space
• Every multiple zeta value is expressible as a linear combination of zeta(k_1,...,k_r) where k_i≥2
• An explicit algorithm for such expansions was developed