On the number of solutions of the linear equation in finite carlitz modules

Chih Nung Hsu; Ting Ting Nan

doi:10.1090/S0002-9939-09-09747-0

On the number of solutions of the linear equation in finite carlitz modules

Chih Nung Hsu^*
, Ting Ting Nan

^*Corresponding author for this work

Department of Mathematics

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

Abstract

We deduce an accurate formula for the number of solutions of the linear equation in generators of finite Carlitz modules, and the equation always has solutions except for some cases. Therefore, we have a criterion for the existence of the solutions of the linear equation. Moreover, we have a similar result in normal bases when we apply our main theorem to a special case.

Original language	English
Pages (from-to)	2191-2200
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	137
Issue number	7
DOIs	https://doi.org/10.1090/S0002-9939-09-09747-0
Publication status	Published - 2009 Jul

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-09-09747-0

Cite this

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abstract = "We deduce an accurate formula for the number of solutions of the linear equation in generators of finite Carlitz modules, and the equation always has solutions except for some cases. Therefore, we have a criterion for the existence of the solutions of the linear equation. Moreover, we have a similar result in normal bases when we apply our main theorem to a special case.",

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AB - We deduce an accurate formula for the number of solutions of the linear equation in generators of finite Carlitz modules, and the equation always has solutions except for some cases. Therefore, we have a criterion for the existence of the solutions of the linear equation. Moreover, we have a similar result in normal bases when we apply our main theorem to a special case.

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On the number of solutions of the linear equation in finite carlitz modules

Abstract

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