PreprintCC BY 4.0arXiv
On Special Arithmetic Gamma Values and Thakur's Gauss Sums: From ∞-adic to v-adic
Abstract
In this paper, we establish an explicit algebra isomorphism between the normalized ∞-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 the phenomenon that Gauss sums, commonly regarded as "finite" analogs of gamma functions, serve as a bridge connecting the ∞-adic and v-adic gamma values.
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BibTeX
@misc{chang2026special,
title = {{On Special Arithmetic Gamma Values and Thakur's Gauss Sums: From $\infty$-adic to $v$-adic}},
author = {Ting-Wei Chang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26398},
eprint = {2610.26398},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26398},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On Special Arithmetic Gamma Values and Thakur's Gauss Sums: From ∞-adic to v-adic
AU - Ting-Wei Chang
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26398
UR - https://arxiv.org/abs/2610.26398
AB - In this paper, we establish an explicit algebra isomorphism between the normalized ∞-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 the phenomenon that Gauss sums, commonly regarded as "finite" analogs of gamma functions, serve as a bridge connecting the ∞-adic and v-adic gamma values.
ER -