In mathematical representation theory, the Eisenstein integral is an integral introduced by Harish-Chandra[1] in the representation theory of semisimple Lie groups, analogous to Eisenstein series in the theory of automorphic forms. Harish-Chandra used Eisenstein integrals to decompose the regular representation of a semisimple Lie group into representations induced from parabolic subgroups.[2] Trombi gave a survey of Harish-Chandra's work on this.[3]
the Eisensteinintegral is an integral introduced by Harish-Chandra in the representation theory of semisimple Lie groups, analogous to Eisenstein series...
Charles Eisenstein (born 1967) is an American public speaker, teacher and author. His work covers a wide range of topics, including the history of human...
In mathematics, a Klingen Eisenstein series is a Siegel modular form of weight k and degree g depending on another Siegel cusp form f of weight k and degree...
In mathematics, the simplest real analytic Eisenstein series is a special function of two variables. It is used in the representation theory of SL(2,R)...
This can be found by using the minimal polynomial and using Eisenstein's criterion. The integral closure of Z in the field of complex numbers C, or the algebraic...
4⌉ = −2. Historically, the floor of x has been–and still is–called the integral part, integer part, or entier of x, often denoted [x] (as well as a variety...
E_{2}(\tau )=1-24\sum _{n}\sigma _{1}(n)q^{n}} is the weight 2 level 1 Eisenstein series (which is a quasimodular form) and σ1(n) is the sum of the divisors...
powerful tool to evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals and infinite series as well...
theorem, which states that if p and q are primary numbers in the ring of Eisenstein integers, both coprime to 3, the congruence x3 ≡ p (mod q) is solvable...
rational root theorem for the case of a monic polynomial. Integral element Gaussian integer Eisenstein integer Root of unity Dirichlet's unit theorem Fundamental...
the fundamental theorem of arithmetic holds. Specifically, a UFD is an integral domain (a nontrivial commutative ring in which the product of any two non-zero...
general principles by means of which he solves a problem proposed by Eisenstein, namely, the decomposition of integer numbers into the sum of five squares;...
is the completion of A. absolute integral closure The absolute integral closure is the integral closure of an integral domain in an algebraic closure of...
In mathematics, a principal ideal domain, or PID, is an integral domain (that is, a commutative ring without nonzero zero divisors) in which every ideal...
in ring theory, a Euclidean domain (also called a Euclidean ring) is an integral domain that can be endowed with a Euclidean function which allows a suitable...
example is the non-real cubic root of unity −1 + √−3/2, which generates the Eisenstein integers. Quadratic integers occur in the solutions of many Diophantine...
are named elliptic functions because they come from elliptic integrals. Those integrals are in turn named elliptic because they first were encountered...
normalization, there is a unique modular form of weight 4 and level 1: the Eisenstein series G4(τ). The theta function for the E8 lattice must then be proportional...
An integer triangle or integral triangle is a triangle all of whose side lengths are integers. A rational triangle is one whose side lengths are rational...
fields; the Gaussian and Eisenstein integers are the simplest examples of these. Gauss develops the arithmetic theory of the "integral complex numbers" and...
the Euler–Mascheroni constant Eulerian integers, more commonly called Eisenstein integers, the algebraic integers of form a + bω where ω is a complex cube...
polynomials with coefficients in an integral domain, and there are two common definitions. Most often, a polynomial over an integral domain R is said to be irreducible...
he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on Fourier series. His contributions to complex...
S2CID 154362112 Eisenstein, Elizabeth L. (1980), The Printing Press as an Agent of Change, Cambridge University Press, ISBN 978-0-521-29955-8 Eisenstein, Elizabeth...
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