On counting polynomials over finite fields
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- by Chih-Yun Chuang, Yen-Liang Kuan and Jing Yu PDF
- Proc. Amer. Math. Soc. 143 (2015), 4305-4316 Request permission
Abstract:
We give an asymptotic formula for the proportion of polynomials of a given degree over a finite field which do not have odd degree irreducible factors. In the case of odd characteristic, this leads to an asymptotic formula for certain weighted partition function which describes the major proportion of the fundamental discriminants where the “negative” Pell equation cannot be solved. We also extend the results to counting positive divisors over an arbitrary global function field.References
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Additional Information
- Chih-Yun Chuang
- Affiliation: Department of Mathematics, National Tsing Hua University, Hsinchu City, Taiwan 300
- Address at time of publication: Taida Institute for Mathematical Sciences, National Taiwan University, Taipei City, Taiwan 10617
- MR Author ID: 1118855
- Email: cychuang@ntu.edu.tw
- Yen-Liang Kuan
- Affiliation: Department of Mathematics, National Taiwan University, Taipei City, Taiwan 10617
- Address at time of publication: Taida Institute for Mathematical Sciences, National Taiwan University, Taipei City, Taiwan 10617
- Email: ylkuan@ntu.edu.tw
- Jing Yu
- Affiliation: Department of Mathematics, National Taiwan University, Taipei City, Taiwan 10617
- Email: yu@math.ntu.edu.tw
- Received by editor(s): February 17, 2014
- Received by editor(s) in revised form: July 21, 2014
- Published electronically: March 31, 2015
- Additional Notes: The authors were supported by NSC grant 102-2119-M-002-187.
- Communicated by: Matthew A. Papanikolas
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 4305-4316
- MSC (2010): Primary 11N45, 11R11, 14H05, 11P81
- DOI: https://doi.org/10.1090/proc/12613
- MathSciNet review: 3373929