Wang-Sun Formula in $\overrightarrow{GL}(\mathbb{Z}/2k\mathbb{Z})$

Octavio A. Agust\'in-Aquino

arXiv:2207.14495·math.NT·October 26, 2023

Wang-Sun Formula in $\overrightarrow{GL}(\mathbb{Z}/2k\mathbb{Z})$

Octavio A. Agust\'in-Aquino

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Abstract

Wang and Sun proved a certain summatory formula involving derangements and primitive roots of the unit. We study such a formula but for the particular case of the set of affine derangements in $G L (Z /2 k Z)$ and its subset of involutive affine derangements in particular; in this last case its value is relatively simple and it is related to even unitary divisors of $k$ .

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TopicsAdvanced Algebra and Geometry · Finite Group Theory Research · Coding theory and cryptography