论文信息 - Sums of Reciprocals of Polynomials over Finite Fields

Sums of Reciprocals of Polynomials over Finite Fields

Abstract We consider the sum of the reciprocals of all monic polynomials of a given degree over a finite field 픽q 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.

[1] Harald Niederreiter,et al. Finite fields: Author Index , 1996 .

[2] Gary L. Mullen,et al. Integers and polynomials: comparing the close cousins Z and Fq[x] , 2005 .

[3] Michael Rosen,et al. A classical introduction to modern number theory , 1982, Graduate texts in mathematics.

[4] K. Conrad,et al. Finite Fields , 2018, Series and Products in the Development of Mathematics.

[5] Dinesh S. Thakur,et al. Power sums with applications to multizeta and zeta zero distribution for Fq[t] , 2009, Finite Fields Their Appl..

[6] Leonard Carlitz,et al. On certain functions connected with polynomials in a Galois field , 1935 .