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 denote the principal congruence subgroup of level 8 and let denote the subgroup of satisfying . 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.

**[1]**A. J. Crisalli,*Theta constants and cusp forms*, Trans. Amer. Math. Soc.**201**(1975), 125–132. MR**0374034**, 10.1090/S0002-9947-1975-0374034-X**[2]**Jun-ichi Igusa,*On the graded ring of theta-constants*, Amer. J. Math.**86**(1964), 219–246. MR**0164967****[3]**Jun-ichi Igusa,*On the graded ring of theta-constants. II*, Amer. J. Math.**88**(1966), 221–236. MR**0200482****[4]**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**

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1975-0398984-3

Keywords:
Congruence subgroup,
cusp form of weight 2,
differential of the first kind,
theta constant

Article copyright:
© Copyright 1975
American Mathematical Society