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On Special Arithmetic Gamma Values and Thakur's Gauss Sums: From $\infty$-adic to $v$-adic
In this paper, we establish an explicit algebra isomorphism between the normalized $\infty$-adic arithmetic gamma values and their $v$-adic counterparts. The construction relies on Thakur's arithmetic Gauss sums, which arise naturally from the Gross-Koblitz-Thakur relations. Our result demonstrates
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