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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On differentials of the first kind and theta constants for certain congruence subgroups

Author: A. J. Crisalli
Journal: Trans. Amer. Math. Soc. 211 (1975), 71-84
MSC: Primary 10D05
MathSciNet review: 0398984
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Abstract: Let $ \Gamma (8)$ denote the principal congruence subgroup of level 8 and let $ \Gamma (16,32)$ denote the subgroup of $ \Gamma (16)$ satisfying $ cd \equiv ab \equiv 0\;(\bmod 32)$. We are dealing only with the elliptic modular case. Consider the spaces of cusp forms of weight 2 (differentials of the first kind) with respect to these groups. It is proved that these spaces are generated by certain monomials of theta constants of degree 4.

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Keywords: Congruence subgroup, cusp form of weight 2, differential of the first kind, theta constant
Article copyright: © Copyright 1975 American Mathematical Society

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