正特征中的多重zeta值：一个Kaneko-Zagier型猜想
Multiple Zeta Values in Positive Characteristic: A Kaneko-Zagier-Type Conjecture
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中文总结 AI 辅助
本文在正特征中构造了∞-进与有限多重zeta值之间的满射比较映射，通过除以ζ_A(q-1)确立Kaneko-Zagier型猜想映射，并证明其与Carlitz多重多对数相容，最终验证了Shi维数猜想的上界。
中文摘要 AI 辅助
本文研究了正特征中$\infty$-进与有限多重zeta值的比较。我们构造了一个从$\infty$-进多重zeta值代数到有限多重zeta值代数之商的满射比较映射。该映射通过除以$\zeta_A(q-1)$的商分解，从而确立了Kaneko-Zagier型猜想映射的良好定义性。我们进一步证明该比较映射与Carlitz多重多对数函数的特殊值以及相应的$\star$-逆值相容。作为应用，我们证明了Shi维数猜想对有限多重zeta值所预测的上界。
英文摘要
In this paper, we study a comparison between $\infty$-adic and finite multiple zeta values in positive characteristic. We construct a surjective comparison map from the algebra of $\infty$-adic multiple zeta values to a quotient of the algebra of finite multiple zeta values. This map factors through the quotient by $ζ_A(q-1)$, thereby establishing the well-definedness of a Kaneko-Zagier-type conjectural map. We further show that the comparison map is compatible with special values of Carlitz multiple polylogarithms, as well as with the corresponding $\star$-inverse values. As an application, we prove the upper bound predicted by Shi's dimension conjecture for finite multiple zeta values.
发表机构
- National Tsing Hua University（国立清华大学）
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