Search Results for ""

Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and ...

A Pisot number is a positive algebraic integer greater than 1 all of whose conjugate elements have absolute value less than 1. A real quadratic algebraic integer greater than ...

Riemann defined the function f(x) by f(x) = sum_(p^(nu)<=x; p prime)1/nu (1) = sum_(n=1)^(|_lgx_|)(pi(x^(1/n)))/n (2) = pi(x)+1/2pi(x^(1/2))+1/3pi(x^(1/3))+... (3) (Hardy ...

An nth-rank tensor in m-dimensional space is a mathematical object that has n indices and m^n components and obeys certain transformation rules. Each index of a tensor ranges ...

The xi-function is the function xi(z) = 1/2z(z-1)(Gamma(1/2z))/(pi^(z/2))zeta(z) (1) = ((z-1)Gamma(1/2z+1)zeta(z))/(sqrt(pi^z)), (2) where zeta(z) is the Riemann zeta ...

A fiber bundle (also called simply a bundle) with fiber F is a map f:E->B where E is called the total space of the fiber bundle and B the base space of the fiber bundle. The ...

The phrase Tomita-Takesaki theory refers to a specific collection of results proven within the field of functional analysis regarding the theory of modular Hilbert algebras ...

Every finite-dimensional Lie algebra of characteristic p=0 has a faithful finite-dimensional representation.

Let G=SL(n,C). If lambda in Z^n is the highest weight of an irreducible holomorphic representation V of G, (i.e., lambda is a dominant integral weight), then the G-map ...

An operator Gamma=sum_(i=1)^me_i^Ru^(iR) on a representation R of a Lie algebra.