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

Hsu, Chih-Nung; Nan, Ting-Ting

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

On the number of solutions of the linear equation in finite Carlitz modules
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by Chih-Nung Hsu and Ting-Ting Nan PDF

Proc. Amer. Math. Soc. 137 (2009), 2191-2200 Request permission

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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