A Carlitz-von Staudt type theorem for finite rings

Khare, Apoorva and Tikaradze, Akaki (2019) A Carlitz-von Staudt type theorem for finite rings. In: LINEAR ALGEBRA AND ITS APPLICATIONS, 568 . pp. 106-126.

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Abstract

We compute the kth power-sums (for all k > 0) over an arbitrary finite unital ring R. This unifies and extends the work of Brawley et al. (1974) 1] for matrix rings, with folklore results for finite fields and finite cyclic groups, and more general recent results of Grau and Oller-Marcen (2017) 12] for commutative rings. As an application, we resolve a conjecture by Fortuny Ayuso et al. (2017) 7] on zeta values for matrix rings over finite commutative rings. We further recast our main result via zeta values over polynomial rings, and end by classifying the translation-invariant polynomials over a large class of finite commutative rings. (C) 2018 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Publication:	LINEAR ALGEBRA AND ITS APPLICATIONS
Publisher:	ELSEVIER SCIENCE INC
Additional Information:	Copyright of this article belongs to ELSEVIER SCIENCE INC
Keywords:	Staudt-Clausen; Power sums; Finite ring; Matrix ring; Translation-invariant polynomial
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	24 May 2019 12:30
Last Modified:	24 May 2019 12:30
URI:	http://eprints.iisc.ac.in/id/eprint/62360

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