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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Chih-Nung Hsu and Ting-Ting Nan
Journal: Proc. Amer. Math. Soc. 137 (2009), 2191-2200
MSC (2000): Primary 11G09; Secondary 11T55, 11T24
Published electronically: January 13, 2009
MathSciNet review: 2495251
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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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Additional Information

Chih-Nung Hsu
Affiliation: Department of Mathematics, National Taiwan Normal University, 88 Sec. 4, Ting-Chou Road, Taipei, Taiwan, Republic of China
Email: maco@math.ntnu.edu.tw

Ting-Ting Nan
Affiliation: Department of Mathematics, National Taiwan Normal University, 88 Sec. 4, Ting-Chou Road, Taipei, Taiwan, Republic of China
Email: ayanami-nan@math.ntnu.edu.tw

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09747-0
PII: S 0002-9939(09)09747-0
Received by editor(s): June 12, 2008
Received by editor(s) in revised form: September 1, 2008
Published electronically: January 13, 2009
Communicated by: Ken Ono
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.