Analytical construction of Weil curves over function fields
Journal de théorie des nombres de Bordeaux, Volume 7 (1995) no. 1, p. 27-49 
@article{JTNB_1995__7_1_27_0,
     author = {Gekeler, Ernst-Ulrich},
     title = {Analytical construction of Weil curves over function fields},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {7},
     number = {1},
     year = {1995},
     pages = {27-49},
     zbl = {0846.11037},
     mrnumber = {1413565},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_1995__7_1_27_0}
}

Gekeler, Ernst-Ulrich. Analytical construction of Weil curves over function fields. Journal de théorie des nombres de Bordeaux, Volume 7 (1995) no. 1, pp. 27-49. http://www.numdam.org/item/JTNB_1995__7_1_27_0/

[1] S. Bosch, W. Lütkebohmert and M. Raynaud, Néron models, Grundlehren. Math. Wiss., Springer, Berlin-New York, 1990. | MR 1045822 | Zbl 0705.14001

[2] P. Deligne, Formes modulaires et representations de GL(2). In: Modular Functions of One Variable II, Lect. Notes Math., vol. 349, Springer, Berlin Heidelberg New York, 1974., pp. 55-105. | MR 347738 | Zbl 0271.10032

[3] P. Deligne and D. Husemöller, Survey of Drinfeld modules., Contemp. Math. 67 (1987), 25-91. | MR 902591 | Zbl 0627.14026

[4] V.G. Drinfeld, Elliptic Modules, Math. Sbornik 94 (1974), 594-627 (Russian); English Translation: Math. USSR-Sbornik 23 (1976), 561-592. | MR 384707 | Zbl 0321.14014

[5] J. Fresnel et M. Van Der Put, Géométrie Analytique Rigide et Applications, Progr. Math., vol. 18, Birkhauser, Basel Boston, 1981. | MR 644799 | Zbl 0479.14015

[6] E.-U. Gekeler, Drinfeld-Moduln und modulare Formen über rationalen Funktionenkörpern, Bonner Math. Schriften 119 (1980). | MR 594434 | Zbl 0446.14018

[7] E.-U. Gekeler, Automorphe Formen über Fq(T) mit kleinem Führer, Abh. Math. Sem. Univ. Hamburg 55 (1985), 111-146. | MR 831522 | Zbl 0564.10026

[8] E.-U. Gekeler, Drinfeld Modular Curves, Lect. Notes Math., vol. 1231, Springer, Berlin Heidelberg New York, 1986. | MR 874338 | Zbl 0607.14020

[9] E.-U. Gekeler, On the coefficients of Drinfeld modular forms, Invent. math. 93 (1988), 667-700. | MR 952287 | Zbl 0653.14012

[10] E.-U. Gekeler et M. Reversat, Jacobians of Drinfeld modular curves, submitted.

[11] L. Gerritzen, On non-archimedean representations of abelian varieties, Math. Ann. 196 (1972), 323-346. | MR 308132 | Zbl 0255.14013

[12] L. Gerritzen and M. Van Der Put, Schottky Groups and Mumford Curves, Lect. Notes Math., vol. 817, Springer, Berlin Heidelberg New York, 1980. | MR 590243 | Zbl 0442.14009

[13] O. Goldmann and N. Iwahori, The space of p-adic norms, Acta Math. 109 (1963),137-177. | MR 144889 | Zbl 0133.29402

[14] D. Goss, π-adic Eisenstein Series for Function Fields, Comp. Math. 41 (1980), 3-38. | Numdam

[15] H. Jacquet and R.P. Langlands, Automorphic forms on GL(2), Lect. Notes Math., vol. 114, Springer, Berlin Heidelberg New York, 1970. | MR 401654 | Zbl 0236.12010

[16] D. Mumford, An analytic construction of degenerating abelian varieties over complete rings, Comp. Math. 24 (1972), 239-272. | Numdam | MR 352106 | Zbl 0241.14020

[17] U. Nonnengardt, Arithmetisch definierte Graphen über rationalen Funktionenkörpern, Diplomarbeit, Saarbrücken (1994).

[18] W. Radtke, Diskontinuierliche Gruppen im Funktionenkörperfall, Dissertation, Bochum (1984).

[19] K. Ribet, Mod p Hecke operators and congruences between modular forms, Invent. Math. 71 (1983), 193-205. | MR 688264 | Zbl 0508.10018

[20] A. Schweizer, Dissertation, in preparation.

[21] J.-P. Serre, Trees, Springer, Berlin- Heidelberg-New York, 1980. | MR 607504 | Zbl 0548.20018

[22] J. Tate, Algorithm for determining the type of a singular fiber in an elliptic pencil. Modular Functions of One Variable IV, Lect. Notes Math., vol. 476, Springer, Berlin Heidelberg New York, 1975, pp. 33-52. | MR 393039

[23] J. Teitelbaum, Modular symbols for Fq(T), Duke Math. J. 68 (1992), 271-295. | MR 1191561 | Zbl 0777.11021

[24] A. Weil, Dirichlet series and automorphic forms, Lect. Notes Math., vol. 189, Springer, Berlin Heidelberg New York, 1971. | Zbl 0218.10046

[25] D. Zagier, Modular parametrizations of elliptic curves, Canad. Math. Bull. 28 (1985), 372-384. | MR 790959 | Zbl 0579.14027