Multiple zeta values of weight at most 2q are linearly independent over F_q, but those of weight 2q+1 satisfy a unique explicit F_q-linear relation.
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math.NT 2years
2026 2verdicts
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Proves Z_q^o generates Z_q and Z_{q,1}^o generates Z_{q,1} via explicit integer relations obtained from finite recursive generating series then taking the limit.
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The threshold for linear independence of multiple zeta values in positive characteristic
Multiple zeta values of weight at most 2q are linearly independent over F_q, but those of weight 2q+1 satisfy a unique explicit F_q-linear relation.
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A unified proof of conjectures on the spaces of multiple $q$-zeta values
Proves Z_q^o generates Z_q and Z_{q,1}^o generates Z_{q,1} via explicit integer relations obtained from finite recursive generating series then taking the limit.