A proof of the Hasse-Weil inequality for genus 2 à la Manin
arXiv:1904.08662
Abstract
We prove the Hasse-Weil inequality for genus 2 curves given by an equation of the form y^2 = f(x) with f a polynomial of degree 5, using arguments that mimic the elementary proof of the genus 1 case obtained by Yu. I. Manin in 1956.
Journal IJPAM, 2019