In [5] Rhoades found linear relations among the Poincaree series of weight k for [[GAMMA].sub.0](N) given by weakly

holomorphic modular forms of weight 2 - k for [[GAMMA].sub.0] (N).

On the order of

holomorphic curves with maximal deficiency sum, II Nobushige TODA Communicated by Masaki KASHIWARA, M.J.A.

Let [OMEGA] be a domain in [C.sup.n] and H([OMEGA]) be the set of

holomorphic mappings from [OMEGA] into [C.sup.n].

Then the difference coordinates [x.sub.j], [[??].sub.j] given by (9)-(10) are

holomorphic functions in the hyperdisc [absolute value of ([xi])] < [square root of (q)], [absolute value of ([eta])] < [square root of (q)] and satisfy (7) if [xi](t), [eta](t) satisfy (8).

where H([OMEGA]) denotes the

holomorphic functions on [beta].

The Privalov class [N.sup.p](U), 1 < p < [infinity], is defined as the set of all

holomorphic functions f on U, satisfying

If f = ([f.sub.1], ..., [f.sub.n]) : D [right arrow] [R.sup.n] is a minimal surface, then there exist

holomorphic functions [g.sub.j] in D such that [f.sub.j] = [Reg.sub.j], 1 [less than or equal to] j [less than or equal to] n.

with f = ([f.sup.1], ..., [f.sup.v]) and F = ([F.sup.1], ..., [F.sup.v]) v-vector functions, [F.sup.i]

holomorphic in a polydisc, say [mathematical expression not reproducible] for some [[rho].sub.1] > [rho] > 0 (here, [D.sub.[rho]]([z.sub.0]) = {z [member of] C : [absolute value of z-[z.sub.0]] < [rho]} denotes an open disc of radius [rho] > 0, centered at [z.sub.0], [[bar.D].sub.[rho]]([z.sub.0]) denotes its closure and [D.sub.[rho]] = [D.sub.[rho]](0)) such that the v x v matrix [A.sub.0] = [F.sub.f](0, 0, 0) is invertible, a condition that makes (1) possess a regular singularity at z = 0.

Now, it is known ([4, 5])--or it could be taken here as a definition--that M is Levi nondegenerate at 0 [member of] M when the local

holomorphic map

It is thanks to the fact that the cohomology class of (2,1)-forms is isomorphic to the cohomology class [H.sup.1/[partial derivative]] (TM), the first Dolbeault cohomology group of M with values in a

holomorphic tangent bundle TM that characterizes infinitesimal complex structure deformations.

Abstract: Suppose that fi is a domain of On , n S 1 , E c f i closed in fi , the Hausdorff measure H2 n -1 (E )= 0 , and f is

holomorphic in fi \ E .