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On counting polynomials over finite fields


Authors: Chih-Yun Chuang, Yen-Liang Kuan and Jing Yu
Journal: Proc. Amer. Math. Soc. 143 (2015), 4305-4316
MSC (2010): Primary 11N45, 11R11, 14H05, 11P81
DOI: https://doi.org/10.1090/proc/12613
Published electronically: March 31, 2015
MathSciNet review: 3373929
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Abstract | References | Similar Articles | Additional Information

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.


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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
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

DOI: https://doi.org/10.1090/proc/12613
Keywords: Asymptotic results, function fields, quadratic extensions, partitions
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
Article copyright: © Copyright 2015 American Mathematical Society

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