On differentials of the first kind and theta constants for certain congruence subgroups
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- by A. J. Crisalli PDF
- Trans. Amer. Math. Soc. 211 (1975), 71-84 Request permission
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.References
- A. J. Crisalli, Theta constants and cusp forms, Trans. Amer. Math. Soc. 201 (1975), 125–132. MR 374034, DOI 10.1090/S0002-9947-1975-0374034-X
- Jun-ichi Igusa, On the graded ring of theta-constants, Amer. J. Math. 86 (1964), 219–246. MR 164967, DOI 10.2307/2373041
- Jun-ichi Igusa, On the graded ring of theta-constants. II, Amer. J. Math. 88 (1966), 221–236. MR 200482, DOI 10.2307/2373057
- Jun-ichi Igusa, Geometric and analytic methods in the theory of theta-functions, Algebraic Geometry (Internat. Colloq., Tata Inst. Fund. Res., Bombay, 1968) Oxford Univ. Press, London, 1969, pp. 241–253. MR 0271117
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 211 (1975), 71-84
- MSC: Primary 10D05
- DOI: https://doi.org/10.1090/S0002-9947-1975-0398984-3
- MathSciNet review: 0398984