Geodesic
Transcendence of analytic parameters of rational elliptic modules
Sbornik. Mathematics, Tome 55 (1986) no. 1, pp. 133-143 Cet article a éte moissonné depuis la source Math-Net.Ru

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The author considers rational elliptic modules over an algebraically closed complete extension $K\supset\mathbf F_q(T)$ and proves that $e(1)$ is transcendental over $\mathbf F_q(T)$ for modules of rank $m. Transcendence of the periods of the lattices corresponding to rational modules of the form $\varphi(t)=T\mathscr F^0+a\mathscr F^m$ is also proved. Bibliography: 3 titles 
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     title = {Transcendence of analytic parameters of rational elliptic modules},
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N. V. Dubovitskaya. Transcendence of analytic parameters of rational elliptic modules. Sbornik. Mathematics, Tome 55 (1986) no. 1, pp. 133-143. http://geodesic.mathdoc.fr/item/SM_1986_55_1_a8/

[1] Wade L. I., “Certain quantities transcendental over $GF(p^n,x)$”, Duke Math. J., 8 (1941), 701–720 | DOI | MR | Zbl

[2] Goss D., “Von Staudt for $\mathbf{F}_q[T]$”, Duke Math. J., 45 (1978), 885–910 | DOI | MR | Zbl

[3] Carlitz L., “On certain functions connected with polynomials in a Galois field”, Duke Math. J., 1 (1935), 137–168 | DOI | MR | Zbl