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 | References | Similar Articles | Additional Information

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

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.