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 algebraic geometry, Horrocks bundles are certain indecomposable rank 3 vector bundles on 5-dimensional projective space, found by Horrocks (1978).
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.
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 (1953) and Maass (1950).
In mathematics, Kummer's congruences are some congruences involving Bernoulli numbers, found by Ernst Eduard Kummer (1851).
In mathematics, a eutactic lattice (or eutactic form) is a lattice in Euclidean space whose minimal vectors form a eutactic star. This means they have a set of positive eutactic coefficientsci such that (v, v) = Σci(v, mi)2 where the sum is over the minimal vectors mi. "Eutactic" is derived from the Greek language, and means "well-situated" or "well-arranged".
In mathematics, the Mehler–Heine formula introduced by Mehler (1868) and Heine (1861) describes the asymptotic behavior of the Legendre polynomials as the index tends to infinity, near the edges of the support of the weight. There are generalizations to other classical orthogonal polynomials, which are also called the Mehler–Heine formula. The formula complements the Darboux formulae which describe the asymptotics in the interior and outside the support.
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 (1839) and rediscovered by Arnold Scholz (1929).
In mathematics, a Remak decomposition, introduced by Remak (1911), is a decomposition of an abelian group or similar object into a finite direct sum of indecomposable objects.
In mathematics, a Prym differential of a Riemann surface is a differential form on the universal covering space that transforms according to some complex character of the fundamental group. Equivalently it is a section of a certain line bundle on the Riemann surface in the same component as the canonical bundle. Prym differentials were introduced by Friedrich Prym (1869).
L. A. Sohnke was a German mathematician who worked on the complex multiplication of elliptic functions.
In mathematics, the Hessian group is a finite group of order 216, introduced by Jordan (1877) who named it for Otto Hesse. It may be represented as the group of affine transformations with determinant 1 of the affine plane over the field of 3 elements. It also acts on the Hesse pencil of elliptic curves, and forms the automorphism group of the Hesse configuration of the 9 inflection points of these curves and the 12 lines through triples of these points.
In algebraic geometry, a Steinerian of a hypersurface, introduced by Steiner (1854), 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 mathematics, an Eisenstein sum is a finite sum depending on a finite field and related to a Gauss sum. Eisenstein sums were introduced by Gotthold Eisenstein (1848), named "Eisenstein sums" by Stickelberger (1890), and rediscovered by Yamamoto (1985), who called them relative Gauss sums.
In mathematics, Jacobsthal sums are finite sums of Legendre symbols related to Gauss sums. They were introduced by Jacobsthal (1907).
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 (1943), 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.
