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Transactions of the American Mathematical Society

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

 
 

 

Theta constants and cusp forms


Author: A. J. Crisalli
Journal: Trans. Amer. Math. Soc. 201 (1975), 125-132
MSC: Primary 10D15
DOI: https://doi.org/10.1090/S0002-9947-1975-0374034-X
MathSciNet review: 0374034
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Abstract: For principal congruence subgroups of levels 2 and 4 a basis for their cusp forms consisting of monomials of theta constants is displayed. Some conditions for the vanishing of Poincaré series of these groups are found.


References [Enhancements On Off] (What's this?)

  • [1] R. C. Gunning, Lectures on modular forms, Ann. of Math. Studies, no. 48, Princeton Univ. Press, Princeton, N. J., 1962. MR 24 #A2664. MR 0132828 (24:A2664)
  • [2] J.-I. Igusa, On the graded ring of theta-constants, Amer. J. Math. 86 (1964), 219-246. MR 29 #2258. MR 0164967 (29:2258)
  • [3] -, On the graded ring of theta-constants. II, Amer. J. Math. 88 (1966), 221-236. MR 34 #375. MR 0200482 (34:375)
  • [4] -, 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 42 #6000. MR 0271117 (42:6000)

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DOI: https://doi.org/10.1090/S0002-9947-1975-0374034-X
Article copyright: © Copyright 1975 American Mathematical Society

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