In mathematics, an Eichler order, named after Martin Eichler, is an order of a quaternion algebra that is the intersection of two maximal orders.
Elwin Bruno Christoffel was a German mathematician and physicist. He introduced fundamental concepts of differential geometry, opening the way for the development of tensor calculus, which would later provide the mathematical basis for general relativity.
In mathematical group theory, the Schur multiplier or Schur multiplicator is the second homology group of a group G. It was introduced by Issai Schur in his work on projective representations.
In algebraic group theory, approximation theorems are an extension of the Chinese remainder theorem to algebraic groups G over global fields k.
In mathematics, especially in the area of algebra known as group theory, the term Z-group refers to a number of distinct types of groups:
Thomas Clausen was a Danish mathematician and astronomer.
In algebraic geometry, Horrocks bundles are certain indecomposable rank 3 vector bundles on 5-dimensional projective space, found by Horrocks (1978).
In algebraic number theory, Leopoldt's conjecture, introduced by H.-W. Leopoldt, states that the p-adic regulator of a number field does not vanish. The p-adic regulator is an analogue of the usual regulator defined using p-adic logarithms instead of the usual logarithms, introduced by H.-W. Leopoldt.
In algebraic geometry, the Kawamata–Viehweg vanishing theorem is an extension of the Kodaira vanishing theorem, on the vanishing of coherent cohomology groups, to logarithmic pairs, proved independently by Viehweg and Kawamata in 1982.
In mathematics, specifically group theory, isoclinism is an equivalence relation on groups which generalizes isomorphism. Isoclinism was introduced by Hall (1940) to help classify and understand p-groups, although it is applicable to all groups. Isoclinism also has consequences for the Schur multiplier and the associated aspects of character theory, as described in Suzuki and Conway et al.. The word "isoclinism" comes from the Greek ισοκλινης meaning equal slope.
Max Koecher was a German mathematician.
In mathematics, a Koecher–Maass series is a type of Dirichlet series that can be expressed as a Mellin transform of a Siegel modular form, generalizing Hecke's method of associating a Dirichlet series to a modular form using Mellin transforms. They were introduced by Koecher and Maass.
In mathematics, Kummer's congruences are some congruences involving Bernoulli numbers, found by Ernst Eduard Kummer.
In mathematics, the Faber polynomialsPm of a Laurent series
In mathematics, Scholz's reciprocity law is a reciprocity law for quadratic residue symbols of real quadratic number fields discovered by Theodor Schönemann and rediscovered by Arnold Scholz.
In algebraic geometry, a Steinerian of a hypersurface, introduced by Steiner, is the locus of the singular points of its polar quadrics.
In mathematics, a quaternary cubic form is a degree 3 homogeneous polynomial in four variables. The zeros form a cubic surface in 3-dimensional projective space.
In mathematical representation theory, a good filtration is a filtration of a representation of a reductive algebraic group G such that the subquotients are isomorphic to the spaces of sections F(λ) of line bundles λ over G/B for a Borel subgroup B. In characteristic 0 this is automatically true as the irreducible modules are all of the form F(λ), but this is not usually true in positive characteristic. Mathieu (1990) showed that the tensor product of two modules F(λ)⊗F(μ) has a good filtration, completing the results of Donkin (1985) who proved it in most cases and Wang (1982) who proved it in large characteristic. Littelmann (1992) showed that the existence of good filtrations for these tensor products also follows from standard monomial theory.
In mathematics, Brandt matrices are matrices, introduced by Brandt, that are related to the number of ideals of given norm in an ideal class of a definite quaternion algebra over the rationals, and that give a representation of the Hecke algebra.
Thomas Ward is a British mathematician who works in ergodic theory and dynamical systems and its relations to number theory.
Andreas Thom is a German mathematician, working on geometric group theory, algebraic topology, ergodic theory of group actions, and operator algebras.