Geodesic
On arithmetic properties of values of theta-constants
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 6, pp. 95-122

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This article describes results about the transcendence and algebraic independence of values of theta constants (Nullthetawerte) and direct methods for proving these results. Values of other functions related to theta constants are discussed. We also present some conjectures and open questions. 
@article{FPM_2005_11_6_a10,
     author = {Yu. V. Nesterenko},
     title = {On arithmetic properties of values of theta-constants},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {95--122},
     publisher = {mathdoc},
     volume = {11},
     number = {6},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2005_11_6_a10/}
}
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Yu. V. Nesterenko. On arithmetic properties of values of theta-constants. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 6, pp. 95-122. http://geodesic.mathdoc.fr/item/FPM_2005_11_6_a10/