An explicit modular equation in two variables for
Authors:
Harvey Cohn and Jesse Deutsch
Journal:
Math. Comp. 50 (1988), 557568
MSC:
Primary 11F41
MathSciNet review:
929553
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Abstract: A system of modular equations of norm 2 had been found for the Hilbert modular function field of in an earlier issue of this journal. Here an analogous system is found for but with the help of MACSYMA. There are special difficulties in the fact that two spaces of Hilbert modular functions exist for that can be interchanged by the modular equations. The equations are also a remarkable example of hidden symmetries in the algebraic manifold which is defined in by the modular equation.
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 J. I. Deutsch, Identities on Modular Forms in Several Variables Derivable from Hecke Transformations, Dissertation, Brown University, 1986.
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 K. B. Gundlach, "Die Bestimmung der Funktionen zu einigen Hilbertschen Modulgruppen," J. Reine Angew. Math., v. 220, 1965, pp. 109153. MR 0193069 (33:1290)
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 S. Nagaoka, "On Hilbert modular forms III," Proc. Japan Acad., v. 59, 1983, pp. 346348. MR 726199 (85g:11039)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198809295534
PII:
S 00255718(1988)09295534
Keywords:
Hilbert modular functions,
modular equation
Article copyright:
© Copyright 1988
American Mathematical Society
