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An automorphic function f(z) of a complex variable z is one which is analytic (except for poles) in a domain D and which is invariant under a countably infinite group of ...

A modular form which is not allowed to have poles in the upper half-plane H or at iinfty.

A cusp form is a modular form for which the coefficient c(0)=0 in the Fourier series f(tau)=sum_(n=0)^inftyc(n)e^(2piintau) (1) (Apostol 1997, p. 114). The only entire cusp ...

An automorphic graph is a distance-transitive graph Gamma for which the automorphism group Aut(Gamma) acts primitively on the vertices of Gamma and is not a complete graph or ...

A number k such that nk^2 has its last digit(s) equal to k is called n-automorphic. For example, 1·5__^2=25__ (Wells 1986, pp. 58-59) and 1·6__^2=36__ (Wells 1986, p. 68), so ...

A function f is said to be an entire modular form of weight k if it satisfies 1. f is analytic in the upper half-plane H, 2. f((atau+b)/(ctau+d))=(ctau+d)^kf(tau) whenever [a ...

A surface given by the form z=F(x,y).

f(z)=k/((cz+d)^r)f((az+b)/(cz+d)) where I[z]>0.

The standard form of a line in the Cartesian plane is given by ax+by=c for real numbers a,b,c in R. This form can be derived from any of the other forms (point-slope form, ...

A trace form on an arbitrary algebra A is a symmetric bilinear form (x,y) such that (xy,z)=(x,yz) for all x,y,z in A (Schafer 1996, p. 24).