Sums of reciprocals of polynomials over finite fields

Kenneth Hicks, Xiang Dong Hou, Gary L. Mullen

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 languageEnglish (US)
Pages (from-to)313-317
Number of pages5
JournalAmerican Mathematical Monthly
Issue number4
StatePublished - Apr 1 2012

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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