On an uncertainty principle for small index subgroups of finite fields

Jesus Alonso Ochoa Arango; Diego Fernando Díaz Padilla

doi:10.1515/math-2025-0178

On an uncertainty principle for small index subgroups of finite fields

Jesus Alonso Ochoa Arango
, Diego Fernando Díaz Padilla

University of Southern California

Research output: Contribution to journal › Article › peer-review

Abstract

In this article, we continue the study of the nonvanishing minors property initiated by Garcia, Karaali, and Katz, for the compressed Fourier matrix attached to a subgroup H H of the multiplicative group of a finite field F q {{\mathbb{F}}}_{q} and a character χ \chi defined over H H. Here, we provide a characterization of this aforementioned property for symmetries arising from an index-3 subgroup H H and a nontrivial character χ \chi.

Original language	English
Article number	20250178
Pages (from-to)	1-8
Number of pages	8
Journal	Open Mathematics
Volume	23
Issue number	1
DOIs	https://doi.org/10.1515/math-2025-0178
State	Published - 02 Sep 2025

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10.1515/math-2025-0178

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KW - Fourier transform

KW - DFT matrix

KW - compressed Fourier transform

KW - nonvanishing minors

KW - uncertainty principle

KW - Gauss sum

KW - finite field

KW - group character

UR - https://www.scopus.com/pages/publications/105014943231

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ER -

On an uncertainty principle for small index subgroups of finite fields

Abstract

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Lie bialgebra structures over the Lie algebra of truncated polynomials

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On an uncertainty principle for small index subgroups of finite fields

Abstract

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Lie bialgebra structures over the Lie algebra of truncated polynomials

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