number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...

, an eigencurve is a rigid analytic curve that parametrizes certain ''p''-adic families of

modular form In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition. The theory ...

s, and an eigenvariety is a higher-dimensional generalization of this. Eigencurves were introduced by , and the term "eigenvariety" seems to have been introduced around 2001 by .

References

* * Modular forms {{numtheory-stub