This paper has appeared in Number theory (Tiruchiropalli, 1996), 41-69,
Contemp. Math. 210, Amer. Math. Soc., Providence, RI, 1998 and so the
dvi version has been removed. Let E be a modular elliptic curve over Q of prime conductor p.
This paper describes a conjectural p-adic analytic construction of a
global point on E over K, where K is a real quadratic field satisfying
suitable conditions. This global point is constructed via modular symbols, i.e.,
special values of L-functions. The conjecture is tested numerically on certain
elliptic curves of conductor 11 and 37.
The conjecture of this paper was suggested by an earlier result of
M. Bertolini and the author, where the field K was imaginary quadratic.
In this case the predicted formula was proved, thanks to the theory of complex
multiplication and the Cerednik-Drinfeld theory of p-adic uniformization
of Shimura curves.