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Sage Days 21: Function Fields Reading List
Ulmer, Elliptic curves with large rank over function fields. Ann. of Math. (2) 155 (2002), no. 1, 295--315.
Ulmer, Elliptic curves and analogies between number fields and function fields. Heegner points and Rankin L-series, 285--315, Math. Sci. Res. Inst. Publ., 49, Cambridge Univ. Press, Cambridge, 2004.
Ulmer, $L$-functions with large analytic rank and abelian varieties with large algebraic rank over function fields. Invent. Math. 167 (2007), no. 2, 379--408.
Papikian, Computation of Heegner Points for Function Fields. Notes from the 2000 Arizona Winter School (A note from the author: "Please keep in mind that I wrote those notes when I was just learning the subject, so they might contain some mistakes.")