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Mixed Hilbert modular forms and families of abelian varieties

Published online by Cambridge University Press:  18 May 2009

Min Ho Lee
Min Ho Lee
Affiliation:
Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614, U.S.A. E-mail address: lee@math.uni.edu
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In [18] Shioda proved that the space of holomorphic 2-forms on a certain type of elliptic surface is canonically isomorphic to the space of modular forms of weight three for the associated Fuchsian group. Later, Hunt and Meyer [6] made an observation that the holomorphic 2-forms on a more general elliptic surface should in fact be identified with mixed automorphic forms associated to an automorphy factor of the form

for z in the Poincaré upper half plane ℋ, g = and χ(g) = , where g is an element of the fundamental group Γ⊂PSL(2, R) of the base space of the elliptic fibration, χ-Γ→SL(2, R) the monodromy representation, and w: ℋ→ℋ the lifting of the period map of the elliptic surface.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 39 , Issue 2 , May 1997 , pp. 131 - 140
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

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