Abstract
We consider the Dirichlet characters for polynomial rings Fq[T] and the associatedL-functions. By Weil's result, the associatedL-functions are all polynomials. Applying Burgess' idea, we obtain an upper bound for the coefficients of theseL-functions. As an application, using our estimates, we obtain an upper bound for the degree of the fundamental unit in real quadratic function fields.
| Original language | English |
|---|---|
| Pages (from-to) | 76-88 |
| Number of pages | 13 |
| Journal | Finite Fields and their Applications |
| Volume | 5 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1999 Jan |
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Keywords
- Dirichlet characters
- Function fields
- L-functions
ASJC Scopus subject areas
- Theoretical Computer Science
- Algebra and Number Theory
- Engineering(all)
- Applied Mathematics
Cite this
Estimates for coefficients of L-functions for function fields. / Hsu, Chih Nung.
In: Finite Fields and their Applications, Vol. 5, No. 1, 01.1999, p. 76-88.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Estimates for coefficients of L-functions for function fields
AU - Hsu, Chih Nung
PY - 1999/1
Y1 - 1999/1
N2 - We consider the Dirichlet characters for polynomial rings Fq[T] and the associatedL-functions. By Weil's result, the associatedL-functions are all polynomials. Applying Burgess' idea, we obtain an upper bound for the coefficients of theseL-functions. As an application, using our estimates, we obtain an upper bound for the degree of the fundamental unit in real quadratic function fields.
AB - We consider the Dirichlet characters for polynomial rings Fq[T] and the associatedL-functions. By Weil's result, the associatedL-functions are all polynomials. Applying Burgess' idea, we obtain an upper bound for the coefficients of theseL-functions. As an application, using our estimates, we obtain an upper bound for the degree of the fundamental unit in real quadratic function fields.
KW - Dirichlet characters
KW - Function fields
KW - L-functions
UR - http://www.scopus.com/inward/record.url?scp=0032607220&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0032607220&partnerID=8YFLogxK
U2 - 10.1006/ffta.1998.0234
DO - 10.1006/ffta.1998.0234
M3 - Article
AN - SCOPUS:0032607220
VL - 5
SP - 76
EP - 88
JO - Finite Fields and Their Applications
JF - Finite Fields and Their Applications
SN - 1071-5797
IS - 1
ER -