Modular Forms For More General Groups
The functional equation, i.e., the behavior of f with respect to z ↦ (az + b)/(cz + d) can be relaxed by requiring it only for matrices in smaller groups.
Read more about this topic: Modular Form
Famous quotes containing the words forms, general and/or groups:
“And what avails it that science has come to treat space and time as simply forms of thought, and the material world as hypothetical, and withal our pretension of property and even of self-hood are fading with the rest, if, at last, even our thoughts are not finalities, but the incessant flowing and ascension reach these also, and each thought which yesterday was a finality, to-day is yielding to a larger generalization?”
—Ralph Waldo Emerson (18031882)
“I suggested to them also the great desirability of a general knowledge on the Island of the English language. They are under an English speaking government and are a part of the territory of an English speaking nation.... While I appreciated the desirability of maintaining their grasp on the Spanish language, the beauty of that language and the richness of its literature, that as a practical matter for them it was quite necessary to have a good comprehension of English.”
—Calvin Coolidge (18721933)
“Trees appeared in groups and singly, revolving coolly and blandly, displaying the latest fashions. The blue dampness of a ravine. A memory of love, disguised as a meadow. Wispy cloudsthe greyhounds of heaven.”
—Vladimir Nabokov (18991977)