Algebras of automorphic forms with few generators
Author:
Philip Wagreich
Journal:
Trans. Amer. Math. Soc. 262 (1980), 367389
MSC:
Primary 10D15; Secondary 14J17, 30F35
MathSciNet review:
586722
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Abstract: Those finitelygenerated Fuchsian groups G for which the graded algebra of automorphic forms A is generated by 2 or 3 elements are classified. In these cases the structure of A is described.
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 I. Dolgachev, Automorphic forms and quasihomogeneous singularities, Functional Anal. Appl. 9 (1975), 149151.
 [D2]
 , Automorphic forms and quasihomogeneous singularities (preprint).
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 [K]
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 J. Milnor, On the 3dimensional Brieskorn manifolds, , Knots, Groups and 3Manifolds (Papers dedicated to the memory of R. H. Fox), Ann. of Math. Studies, no. 84, Princeton Univ. Press, Princeton, N. J., 1975, pp. 175225. MR 0418127 (54:6169)
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 P. Orlik and P. Wagreich, Algebraic surfaces with action, Acta Math. 138 (1977), 4381. MR 0460342 (57:336)
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 B. SaintDonat, On Petri's analysis of the linear system of quadrics through a canonical curve, Math. Ann. 206 (1973), 157175. MR 0337983 (49:2752)
 [S]
 G. Springer, Introduction to Riemann surfaces, AddisonWesley, Reading, Mass., 1957. MR 0092855 (19:1169g)
 [W1]
 P. Wagreich, Elliptic singularities of surfaces, Amer. J. Math. 92 (1970), 419454. MR 0291170 (45:264)
 [W2]
 , Automorphic forms and singularities with action, Illinois J. Math. (to appear).
 [Z]
 O. Zariski and P. Samuel, Commutative algebra. I, Van Nostrand, Princeton, N. J., 1959.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198005867222
PII:
S 00029947(1980)05867222
Keywords:
Automorphic form,
Fuchsian group,
graded ring,
Poincaré power series
Article copyright:
© Copyright 1980
American Mathematical Society
