Abstract
Let $$\mathcal{X}$$ be a projective irreducible nonsingular algebraic curve defined over a finite field $$\mathbb{F}_q$$ . This paper presents a variation of the Stohr–Voloch theory and sets new bounds to the number of $${F_{{q^r}}}$$ -rational points on X. In certain cases, where comparison is possible, the results are shown to improve other bounds such as Weil’s, Stohr–Voloch’s and Ihara’s.
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