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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

An explicit modular equation in two variables for $ {\bf Q}(\sqrt3)$


Authors: Harvey Cohn and Jesse Deutsch
Journal: Math. Comp. 50 (1988), 557-568
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 $ {\mathbf{Q}}(\sqrt 2 )$ in an earlier issue of this journal. Here an analogous system is found for $ {\mathbf{Q}}(\sqrt 3 )$ but with the help of MACSYMA. There are special difficulties in the fact that two spaces of Hilbert modular functions exist for $ {\mathbf{Q}}(\sqrt 3 )$ that can be interchanged by the modular equations. The equations are also a remarkable example of hidden symmetries in the algebraic manifold $ {{\mathbf{V}}_2}$ which is defined in $ {{\mathbf{C}}^4}$ by the modular equation.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1988-0929553-4
PII: S 0025-5718(1988)0929553-4
Keywords: Hilbert modular functions, modular equation
Article copyright: © Copyright 1988 American Mathematical Society