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In 1976, Coates and Wiles showed that elliptic curves with complex multiplication having an infinite number of solutions have L-functions which are zero at the relevant fixed ...

Complex infinity is an infinite number in the complex plane whose complex argument is unknown or undefined. Complex infinity may be returned by the Wolfram Language, where it ...

A generalization of Poncelet's continuity principle made by H. Schubert in 1874-1879. The conservation of number principle asserts that the number of solutions of any ...

A fractal curve of infinite length which bounds an area twice that of the original square.

A natural number n>3 such that n|(a^(n-2)-a) whenever (a,n)=1 (a and n are relatively prime) and a<=n. (Here, n|m means that n divides m.) There are an infinite number of ...

The system of partial differential equations iu_t+u_(xx)+alphau_(yy)+betau|u|^2-uv=0 v_(xx)+gammav_(yy)+delta(|u|^2)_(yy)=0.

A curve which can be turned continuously inside an equilateral triangle. There are an infinite number of delta curves, but the simplest are the circle and lens-shaped ...

A directed infinity in direction z is an infinite numerical quantity that is a positive real multiple of the complex number z. Directed infinity may be returned in the ...

The series sumf(n) for a monotonic nonincreasing f(x) is convergent if lim_(x->infty)^_(e^xf(e^x))/(f(x))<1 and divergent if lim_(x->infty)__(e^xf(e^x))/(f(x))>1.

The degree (or relative degree, or index) of an extension field K/F, denoted [K:F], is the dimension of K as a vector space over F, i.e., [K:F]=dim_FK. If [K:F] is finite, ...