Sums of reciprocals of polynomials over finite fields

Kenneth Hicks; Xiang Dong Hou; Gary L. Mullen

doi:10.4169/amer.math.monthly.119.04.313

Sums of reciprocals of polynomials over finite fields

Kenneth Hicks, Xiang Dong Hou, Gary L. Mullen

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We consider the sum of the reciprocals of all monic polynomials of a given degree over a finite field Fq each raised to the power of k. When k ≤ q, the sum has a surprisingly simple result due to mysterious cancellations that occur in the sum.We discuss this interesting phenomenon and provide a new inductive proof.

Original language	English (US)
Pages (from-to)	313-317
Number of pages	5
Journal	American Mathematical Monthly
Volume	119
Issue number	4
DOIs	https://doi.org/10.4169/amer.math.monthly.119.04.313
State	Published - Apr 2012

All Science Journal Classification (ASJC) codes

General Mathematics

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10.4169/amer.math.monthly.119.04.313

Cite this

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AB - We consider the sum of the reciprocals of all monic polynomials of a given degree over a finite field Fq each raised to the power of k. When k ≤ q, the sum has a surprisingly simple result due to mysterious cancellations that occur in the sum.We discuss this interesting phenomenon and provide a new inductive proof.

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Sums of reciprocals of polynomials over finite fields

Abstract

All Science Journal Classification (ASJC) codes

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