A Congruence Satisfied by the Theta-constant 0,
نویسنده
چکیده
where the denominators of the bn are powers of 2. If we substitute from (3) into (1) we get a certain set of congruences; if we substitute from (4) we get another set. By Lemma 1 of [l ] these congruences are equivalent. We now show how the second substitution can be carried out explicitly. We recall that the complete elliptic integral of the first kind is given by TT / 1 1 \ K = — F[ —, —; l;k2), 2 \2 2 /
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