Extending Nathanson Heights to Arbitrary Finite Fields
نویسنده
چکیده
In this paper, we extend the definition of the Nathanson height from points in projective spaces over Fp to points in projective spaces over arbitrary finite fields. If [a0 : . . . : an] ∈ P(Fp), then the Nathanson height is hp([a0 : a1 : . . . : ad]) = min b∈Fp d ∑ i=0 H(bai) where H(ai) = |N(ai)|+p(deg(ai)−1) with N the field norm and |N(ai)| the element of {0, 1, . . . , p− 1} congruent to N(ai) modulo p. We investigate the basic properties of this extended height, provide some bounds, study its image on the projective line hp(P(Fp)) and propose some questions for further research.
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