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arXiv · 2406.18890

Spectral dimension of $p$-adic integers

Surajit Biswas·Bipul Saurabh
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Abstract

The notion of spectral dimension was introduced by Chakraborty and Pal in \cite{cp}. In this paper, we show that the spectral dimension of the ring of $p$-adic integers, $\mathbb{Z}_p$, is equal to its manifold dimension, which is $0$. Finally, we determine the $K$-groups of $\mathbb{Z}_p$, and show that the generators of $K_0(\mathbb{Z}_p)$ can be expressed as finite span of the characters of $\mathbb{Z}_p$.

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Surajit Biswas, Bipul Saurabh. 2024-06-27. Spectral dimension of $p$-adic integers. https://arxiv.org/abs/2406.18890

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