Remote Access Mathematics of Computation
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

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

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 11F41

Retrieve articles in all journals with MSC: 11F41

Additional Information

Keywords: Hilbert modular functions, modular equation
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society