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p-adic entropy and a p-adic Fuglede-Kadison determinant

C. Deninger
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Abstract

Using periodic points we study a notion of entropy with values in the p-adic numbers. This is done for actions of countable discrete residually finite groups $Γ$. For suitable $Γ= \mathbb{Z}^d$-actions we obtain p-adic analogues of multivariable Mahler measures. For certain actions of more general groups the p-adic entropy can be expressed in terms of a p-adic analogue of the Fuglede-Kadison determinant from the theory of von Neumann algebras. Many basic questions remain open.

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C. Deninger. 2007-10-19. p-adic entropy and a p-adic Fuglede-Kadison determinant. https://arxiv.org/abs/math/0608539

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