modularity of elliptic curves
... An unrestricted modular form is an analytic function whose domain consists of the complex numbers whose imaginary parts are positive. An unrestricted modular form’s range is the set of all complex numbers. f(z) is an unrestricted modular form of weight w if and only if f((az+b)/(cz+d)) = (cz+d)wf(z) ...
... An unrestricted modular form is an analytic function whose domain consists of the complex numbers whose imaginary parts are positive. An unrestricted modular form’s range is the set of all complex numbers. f(z) is an unrestricted modular form of weight w if and only if f((az+b)/(cz+d)) = (cz+d)wf(z) ...
Commutative ring
... A particularly important type of ideals are prime ideals, often denoted p. This notion arose when algebraists (in the 19th century) realized that, unlike in Z, in many rings there is no unique factorization into prime numbers. (Rings where it does hold are called unique factorization domains.) By de ...
... A particularly important type of ideals are prime ideals, often denoted p. This notion arose when algebraists (in the 19th century) realized that, unlike in Z, in many rings there is no unique factorization into prime numbers. (Rings where it does hold are called unique factorization domains.) By de ...
