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arXiv · 2311.04805

On a product formula of bivariate $p$-adic Gamma values

Luochen Zhao
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Abstract

We establish a derivative formula of $p$-adic Shintani $L$-functions, thus those of totally real $p$-adic Hecke $L$-functions with trivial moduli. As an application, we present a product formula of bivariate $p$-adic Gamma values by specializing to genus $L$-functions, which takes a particularly simple form when the field is $\mathbf{Q}(\sqrt{3})$. In the appendix we explain how the product formula is supposed to encode a higher analytic analogue of the Davenport-Hasse relation.

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Luochen Zhao. 2023-11-08. On a product formula of bivariate $p$-adic Gamma values. https://arxiv.org/abs/2311.04805

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