JP Journal of Algebra, Number Theory and Applications
Volume 32, Issue 2, Pages 141 - 164
(March 2014)
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A NOTE ON POWER SUMS OVER FINITE FIELDS
Javier Diaz-Vargas and Eduardo Hernandez-Mezquita
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Abstract: We study basic aspects of the sums of nonpositive integral powers of monic polynomials of degree one over a finite field. The combinatorics of cancelation in these sums is rather complicated. The focus is basically on the valuations of these sums in the infinite place of where q is a power of a prime p. We present the concept of integer with inner q carry over of depth j. For exponents of the form relative prime to p and k relative prime to q, where k presents inner q carry over of depth j, we give a result to find the valuation at the infinite place of of the sums of powers under study, for any finite field. |
Keywords and phrases: finite fields, power sums, zeta function. |
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