An explicit modular equation in two variables for

Authors:
Harvey Cohn and Jesse Deutsch

Journal:
Math. Comp. **50** (1988), 557-568

MSC:
Primary 11F41

MathSciNet review:
929553

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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 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.

**[1]**Harvey Cohn,*An explicit modular equation in two variables and Hilbert’s twelfth problem*, Math. Comp.**38**(1982), no. 157, 227–236. MR**637301**, 10.1090/S0025-5718-1982-0637301-5**[2]**Harvey Cohn,*Successive diagonal projections of Hilbert modular functions*, Number theory (New York, 1984–1985) Lecture Notes in Math., vol. 1240, Springer, Berlin, 1987, pp. 69–86. MR**894504**, 10.1007/BFb0072973**[3]**Harvey Cohn and Jesse Deutsch,*Application of symbolic manipulation to Hecke transformations of modular forms in two variables*, Math. Comp.**48**(1987), no. 177, 139–146. MR**866104**, 10.1090/S0025-5718-1987-0866104-6**[4]**J. I. Deutsch,*Identities on Modular Forms in Several Variables Derivable from Hecke Transformations*, Dissertation, Brown University, 1986.**[5]**Karl-Bernhard Gundlach,*Die Bestimmung der Funktionen zu einigen Hilbertschen Modulgruppen*, J. Reine Angew. Math.**220**(1965), 109–153 (German). MR**0193069****[6]**Shōyū Nagaoka,*On Hilbert modular forms. III*, Proc. Japan Acad. Ser. A Math. Sci.**59**(1983), no. 7, 346–348. MR**726199**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1988-0929553-4

Keywords:
Hilbert modular functions,
modular equation

Article copyright:
© Copyright 1988
American Mathematical Society