\providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace}
\providecommand{\MR}{\relax\ifhmode\unskip\space\fi MR }
% \MRhref is called by the amsart/book/proc definition of \MR.
\providecommand{\MRhref}[2]{%
  \href{http://www.ams.org/mathscinet-getitem?mr=#1}{#2}
}
\providecommand{\href}[2]{#2}
\begin{thebibliography}{BCDT01}

\bibitem[ASD73]{artin-sd}
M.~Artin and P.~Swinnerton-Dyer, \emph{The {S}hafarevich-{T}ate conjecture for
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C.~Breuil, B.~Conrad, F.~Diamond, and R.~Taylor, \emph{On the modularity of
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\bibitem[BD98]{bd98}
M.~Bertolini and H.~Darmon, \emph{Heegner points, p-adic {L}-functions, and the
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\bibitem[Bro94]{bro94}
M.~Brown, \emph{On a conjecture of {T}ate for elliptic surfaces over finite
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\bibitem[Del73]{del73}
P.~Deligne, \emph{Les constantes des \'{e}quations fonctionnelles des fonctions
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\bibitem[DH87]{dh87}
P.~Deligne and D.~Husemoller, \emph{Survey of drinfeld modules}, Current trends
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\bibitem[Dri74]{dri74}
V.\thinspace{}G. Drinfeld, \emph{Elliptic modules}, Mat. Sb. (N.S.) \textbf{94
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\bibitem[GR96]{gr96}
E.-U. Gekeler and M.~Reversat, \emph{Jacobians of drinfeld modular curves}, J.
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\bibitem[GZ86]{gross-zagier}
B.~Gross and D.~Zagier, \emph{Heegner points and derivatives of
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  \MR{87j:11057}

\bibitem[Kat02]{kat02}
N.~Katz, \emph{Twisted {L}-functions and monodromy}, Annals of Mathematics
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\bibitem[Kol90]{kol90}
V.~Kolyvagin, \emph{Euler systems}, The Grothendieck Festschrift, Vol. II,
  Progr. Math., vol. 87, Birkh\"{a}user Boston, Boston, 1990, pp.~435--483.

\bibitem[Lon02]{lon02}
I.~Longhi, \emph{Non-{A}rchimedean integration and elliptic curves over
  function fields}, J. Number Theory \textbf{94} (2002), 375--404.

\bibitem[MB85]{mb85}
L.~Moret-Bailly, \emph{Pinceaux de vari\'{e}t\'{e}s ab\'{e}liennes},
  Ast\'{e}rique \textbf{no. 129,266} (1985), 31--34.

\bibitem[Mil75]{milne:artintate}
J.\thinspace{}S. Milne, \emph{On a conjecture of {A}rtin and {T}ate}, Ann. of
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\bibitem[Mil80]{milne:etale}
\bysame, \emph{\'{E}tale cohomology}, Princeton University Press, Princeton,
  N.J., 1980. \MR{81j:14002}

\bibitem[MM00]{mm00}
R.~Martin and W~McMillen, \emph{An elliptic curve over \protect{$\Q$} with rank
  at least 24}, Number Theory Listserver (2000).

\bibitem[P\'00]{pal00}
A.~P\'{a}l, \emph{Drinfeld modular curves, heegner points and interpolation of
  special values}, Columbia University Ph.D. thesis (2000).

\bibitem[Ros02]{rosen:ff}
M.~Rosen, \emph{Number theory in function fields}, Springer, New York, 2002.

\bibitem[RT00]{rt00}
H.-G. R\"{u}ck and U.~Tipp, \emph{Heegner points and {L}-series of automorphic
  cusp forms of drinfeld type}, Doc. Math. \textbf{5} (2000), 365--444
  (electronic).

\bibitem[Shi86]{shi86}
T.~Shioda, \emph{An explicit algorithm for computing the picard number of
  certain algebraic surfaces}, Amer. J. Math \textbf{108} (1986), 415--432.

\bibitem[Sil92]{silverman:aec}
J.\thinspace{}H. Silverman, \emph{The arithmetic of elliptic curves},
  Springer-Verlag, New York, 1992, Corrected reprint of the 1986 original.

\bibitem[Sti93]{codes}
H.~Stichtenoth, \emph{Algebraic function fields and codes}, Springer-Verlag,
  Berlin, 1993.

\bibitem[Tat65]{t65}
J.~Tate, \emph{Algebraic cycles and poles of zeta functions}, Arithmetical
  Algebraic Geometry (O. F. G. Schilling, ed.), Harper and Row, New York, 1965,
  pp.~93--110.

\bibitem[Tat94]{tate:ladic}
\bysame, \emph{Conjectures on algebraic cycles in l-adic cohomology}, Motives
  (Seattle, WA, 1991), Proc. Sympos. Pure Math., vol. 55, Amer. Math. Soc.,
  Providence, RI, 1994, pp.~71--83.

\bibitem[Tat95]{tate:bsd}
\bysame, \emph{On the conjectures of {B}irch and {S}winnerton-{D}yer and a
  geometric analog}, S\'eminaire Bourbaki, Vol.\ 9, Soc. Math. France, Paris,
  1995, pp.~Exp.\ No.\ 306, 415--440.

\bibitem[TS67]{ts67}
J.~Tate and I.~Shafarevich, \emph{The rank of elliptic curves}, Dokl. Akad.
  Nauk SSSR \textbf{175} (1967), 770--773.

\bibitem[Ulm]{ulmer:a}
D.~Ulmer, \emph{Automorphic forms on \protect{${\rm {G}{L}}(2)$} over function
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\bibitem[Ulm02]{ulmer:highrank}
\bysame, \emph{Elliptic curves with large rank over function fields}, Ann. of
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\bibitem[Ulm03]{ulmer:nonvan}
\bysame, \emph{Geometric non-vanishing}, preprint (2003).

\bibitem[Ulm04]{ulmer:analogies}
\bysame, \emph{Elliptic curves and analogies between number fields and function
  fields}, Heegner points and {R}ankin {L}-series {(MSRI) P}ublications 48,
  Cambridge Univ. Press, New York, 2004, pp.~??--??

\bibitem[Wei71]{weil71}
A.~Weil, \emph{Dirichlet series and automorphic {L}-forms}, Lecture Notes in
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\bibitem[Wil00]{wiles:cmi}
A.\thinspace{}J. Wiles, \emph{The {B}irch and {S}winnerton-{D}yer
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\bibitem[Zar74]{zar74}
Y.~Zarhin, \emph{A finiteness theorem for isogenies of abelian varieties over
  function fields of finite characteristic ({R}ussian)}, Funkcional. Anal. i
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\end{thebibliography}
