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We outline an algorithm to compute θ(z, τ ) in genus 2 in quasi-optimal time, borrowing ideas from the algorithm for theta constants and the one for θ(z, τ ) in genus 1. Our implementation shows a l...
In \cite{LuRo2010}, Lubicz and Robert generalized the Tate pairing over any abelian variety and more precisely over Theta functions. The security of the new algorithms is an important issue for the us...
In 1986, D. V. Chudnovsky and G. V. Chudnovsky proposed to use formulae coming from Theta functions for the arithmetic in Jacobians of genus 2 curves. We follow this idea and derive fast formulae fo...
We have discovered conjectural near-addition formulas for Somos sequences. We have preliminary evidence suggesting the existence of modular theta functions.

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