Analytical construction of Weil curves over function fields
Journal de théorie des nombres de Bordeaux, Tome 7 (1995) no. 1, pp. 27-49 
@article{JTNB_1995__7_1_27_0,
     author = {Ernst-Ulrich Gekeler},
     title = {Analytical construction of {Weil} curves over function fields},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {27--49},
     year = {1995},
     publisher = {Universit\'e Bordeaux I},
     volume = {7},
     number = {1},
     zbl = {0846.11037},
     mrnumber = {1413565},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_1995__7_1_27_0/}
}
TY  - JOUR
AU  - Ernst-Ulrich Gekeler
TI  - Analytical construction of Weil curves over function fields
JO  - Journal de théorie des nombres de Bordeaux
PY  - 1995
SP  - 27
EP  - 49
VL  - 7
IS  - 1
PB  - Université Bordeaux I
UR  - https://jtnb.centre-mersenne.org/item/JTNB_1995__7_1_27_0/
LA  - en
ID  - JTNB_1995__7_1_27_0
ER  - 
%0 Journal Article
%A Ernst-Ulrich Gekeler
%T Analytical construction of Weil curves over function fields
%J Journal de théorie des nombres de Bordeaux
%D 1995
%P 27-49
%V 7
%N 1
%I Université Bordeaux I
%U https://jtnb.centre-mersenne.org/item/JTNB_1995__7_1_27_0/
%G en
%F JTNB_1995__7_1_27_0
Ernst-Ulrich Gekeler. Analytical construction of Weil curves over function fields. Journal de théorie des nombres de Bordeaux, Tome 7 (1995) no. 1, pp. 27-49. https://jtnb.centre-mersenne.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. | Zbl | MR

[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. | Zbl | MR

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

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

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

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

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

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

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

[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. | Zbl | MR

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

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

[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. | Zbl | MR

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

[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. | Zbl | MR

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

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

[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

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

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

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