Is the number $\sum\_{n=1}^\infty \frac{1}{2^{n^2}}$ known to be transcendental?


Is there a survey with up-to-date transcendence results?



Is this number already known to be transcendental? Is there a survey about up-to-date trascendence results?
I have checked with [*Introduction to Algebraic Independence Theory*](http://books.google.com.ua/books?id=liYae-vUZs4C&printsec=frontcover&dq=introduction+to+algebraic+independence+theory&source=bl&ots=6Kf4QYSDlS&sig=bJ2TfJ5Fi54ktqf56svrBYIkXyk&hl=en&ei=2BNZTfDtAcWSOq_PpPoE&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBcQ6AEwAA#v=onepage&q&f=false), where it is mentioned in the preface (p. V) that



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> D. Bertrand and independently D. Duverney, Ke. Nishioka, Ku. Nishioka, I. Shiokawa (DNNS) deduced results on algebraic independence of the values of theta-functions at algebraic points and in particular derived the transcendence of the sums $\sum\_{n=1}^\infty q^{n^2}$ for any algebraic $q$ satisfying $0 < |q| < 1$.
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The precise references are not given but a little googling turned up the paper by D. Bertrand, [Theta Functions and Transcendence](https://rdcu.be/cQ61t), *The Ramanujan Journal*, Vol. 1 (1997), pp. 339-350, which seems to be relevant. The second reference is DNNS, [Transcendence of Jacobi's theta series](https://projecteuclid.org/journalArticle/Download?urlId=10.3792%2Fpjaa.72.202), *Proc. Japan Acad. Ser. A Math. Sci.*, Vol. 72 (1996), pp. 202-203.


