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The main purpose of the present paper consists in providing a straightforward proof of Carleman estimates for second order elliptic operators with real coef- ficients in the

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We improve their genus 2 case algorithm, generalize it for genus 3 hyperelliptic curves and introduce a way to deal with the genus 3 non-hyperelliptic case, using algebraic

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The aim of this work is to reveal properties of the classical Jacobi theta functions looked at on a logarithmic scale as well as setting known results into a new context..