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A bound on the number of points of a plane curve. (English) Zbl 1185.14017
Summary: A conjecture is formulated for an upper bound on the number of points in PG$$(2,q)$$ of a plane curve without linear components, defined over GF$$(q)$$. We prove a new bound which is half-way from the known bound to the conjectured one. The conjecture is true for curves of low or high degree, or with rational singularity.

##### MSC:
 14G15 Finite ground fields in algebraic geometry 14H25 Arithmetic ground fields for curves
##### Keywords:
plane curve; projective plane
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##### References:
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