1,733 articles
List of mathematical series
The list of mathematical series, also covering partial sum formulae, collects the important named series such as the geometric, harmonic, and zeta series, with their convergence and sums.
List of number fields with class number one
The list of number fields with class number one covers rings of integers with unique factorization, including the nine imaginary quadratic discriminants 3, 4, 7, 8, 11, 19, 43, 67, and 163.
List of numbers
A list of numbers is a reference catalog of notable numbers, organized by number type, named classes like perfect numbers, and mathematical constants such as π and e.
List of prime numbers
The list of prime numbers is the infinite ordered sequence 2, 3, 5, 7, 11, 13, and so on: integers greater than 1 divisible only by 1 and themselves.
List of publications in mathematics
The list of publications in mathematics is a curated record of the mathematical literature, from Euclid's Elements of 300 BC to modern reviewing databases like MathSciNet and zbMATH Open.
List of representations of e
The list of representations of e collects the infinite series, limits, continued fractions, and infinite products converging to e, the base of the natural logarithm, equal to about 2.71828.
List of types of numbers
Types of numbers are sets of mathematical objects with operations obeying specified rules, classified by hierarchy, algebraic properties, integer properties, and numeral systems used to write them.
Littlewood conjecture
The Littlewood conjecture is an open problem in Diophantine approximation, stating that every pair of real numbers can be simultaneously approximated by rationals with the same denominator.
Littlewood–Richardson rule
The Littlewood–Richardson rule is a combinatorial rule for computing the Littlewood–Richardson coefficients that expand products of Schur functions, stated by Littlewood and Richardson in 1934.
LLL lattice reduction
LLL lattice reduction is a 1982 algorithm by Lenstra, Lenstra, and Lovász that turns a lattice basis into short, nearly orthogonal vectors in polynomial time.
LMFDB
The LMFDB (L-functions and Modular Forms Database) is an open-source online database at www.lmfdb.org cataloging L-functions, modular forms, and related mathematical objects, first released in 2016.
Local class field theory
Local class field theory is the part of number theory that classifies abelian extensions of a local field, identifying their Galois groups with quotients of the field's multiplicative group.
Local cohomology
Local cohomology is a construction in commutative algebra, introduced by Grothendieck in the early 1960s, whose functors measure a module's behavior near a closed set and test depth.
Local field
A local field in algebraic number theory is a field complete with respect to a discrete valuation and having a finite residue field, such as the p-adic numbers.
Local ring
A local ring, also known as a quasi-local or quasilocal ring, is a ring with exactly one maximal ideal, the basic algebraic tool for studying geometric objects near a single point.
Localization (ring theory)
Localization is a construction in commutative algebra that inverts a multiplicative set S in a ring, producing fractions S⁻¹A; at a prime ideal it yields a local ring.
Locally compact group
A locally compact group, also called a locally compact topological group, is a topological group where every point has a compact neighborhood. It is the standard setting for Haar measure and harmonic analysis.
Log
A log, or logarithm, is the exponent a fixed base must be raised to produce a number, turning multiplication into addition; Napier published it in 1614.
Log scheme
A log scheme is a scheme equipped with a logarithmic structure, a sheaf of commutative monoids recording boundary or degeneration data, introduced by Kato in 1989.
Logarithm tables
Logarithm tables are printed lists pairing numbers with their logarithms so multiplication and division can be done by addition and subtraction, standard from John Napier's first table of 1614 until calculators spread in the 1970s.
Logarithmic integral function
The logarithmic integral, li(x), is a special function defined as the integral of 1/ln t for x > 1, used as the standard approximation to the prime counting function π(x).
Lonely runner conjecture
The Lonely Runner Conjecture, or lonely runner problem, is an unsolved number theory problem posed by Jörg M. Wills in 1967 concerning runners on a unit circle.](20 words)
Long and short scales
The long and short scales are two competing systems for naming large numbers: in the short scale each new term is 1,000 times the previous one, in the long scale 1,000,000 times.
Long division
Long division is a standard method for dividing multi-digit numbers by hand, breaking the problem into a series of steps and allowing arbitrarily large numbers to be computed on paper.
Look-and-say sequence
The look-and-say sequence, also called the Conway sequence or audioactive decay, is an integer sequence where each term describes the previous one, giving 1, 11, 21, 1211, 111221.
Loop algebra
A loop algebra is an infinite-dimensional Lie algebra formed from a Lie algebra by extending its scalars to Laurent polynomials, and it underlies affine Kac-Moody algebras.
Low-density parity-check code
A low-density parity-check (LDPC) code is an error-correcting code defined by a sparse parity-check matrix, proposed by Robert G. Gallager at MIT in 1960 and used in 5G, Wi-Fi, and satellite broadcasting.
Low-rank approximation
A low-rank approximation replaces a matrix with one of much lower rank that preserves its dominant structure, used for compression, denoising, and fast linear algebra on large data matrices.
Lowest common denominator
The lowest common denominator (LCD), also called the least common denominator, is the least common multiple of the denominators in a set of fractions, used mainly to add and subtract fractions with unlike denominators.
LU decomposition
The LU decomposition, also called LU factorization or LR decomposition, expresses a matrix as the product of a lower triangular matrix L and an upper triangular matrix U.