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I know there is a contruction of the p-adic sigma function due to Tate and Mazur for curves with ordinary reduction. I think this has been generalized to more cases, do you know of a good (accesible) reference about it? I am particularly interested in the following:

Let $K$ be a finite extension of $\mathbb{Q}_p$, $N=p^n$ and E/K and elliptic curve whose N-torsion points have coordinates in K. For an N-torsion point $e\in E$ I am interested in expressing the function $f_e$, $div(f_e)=N(e)-N(0)$, with values restricted to the formal group of E, as a product of sigma (Theta) functions.

I would like to know a big picture about the p-adic theta functions, and the recent constructions


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