On the classification of elliptic surfaces withq=1
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We classify, up to isomorphism, elliptic surfaces with irregularity one having exactly one singular fiber (necessarily of type I6*). All of them turn out to be elliptic modular surfaces (Shioda [11]), so that the problem is indirectly equivalent to classifying certain subgroups of SL2(Z). These surfaces are then used to produce examples of (elliptic) surfaces with q=1, any pg1, which have maximal Picard number (see Persson [7] for the case q=0). Finally, the classification yields some interesting relationships between hypergeometric functions, theta functions, and certain automorphic forms. 1988 Springer-Verlag.
