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Bounds for the number of points on curves over finite fields (1608.05039v1)
Published 17 Aug 2016 in math.AG and math.NT
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 St\"orh-Voloch theory and sets new bounds to the number of $\mathbb{F}{qr}$-rational points on $\mathcal{X}$. In certain cases, where comparison is possible, the results are shown to improve other bounds such as Weil's, St\"orh-Voloch's and Ihara's.
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