The Elliptic Modular Functions Associated With the Elliptic Norm Curve E7 (Classic Reprint)

Excerpt from The Elliptic Modular Functions Associated With the Elliptic Norm Curve E7

The cases considered by Dr. Miller are relatively simple due to the fact that the modular group is of genus zero. In this paper the case n 7 for which the genus is three, one which is fairly typical of the general case, is subjected to a similar investigation. Many of the results may be extended easily to the case where n is any prime number, or in some features to the case where n is any odd num ber. In this discussion from the standpoint of geometry and group theory, we derive the well known elliptic modular functions attached to this group as well as some new ones and obtain a number of their algebraic properties.

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