1,733 articles
L-infinity
L-infinity, written L^∞, is the Banach space of essentially bounded measurable functions on a measure space, normed by the essential supremum and forming the endpoint of the L^p family.
Lagrange's four-square theorem
Lagrange's four-square theorem, also known as Bachet's conjecture, states that every positive integer is a sum of at most four squares of integers, first proved by Lagrange in 1770.
Lagrange's theorem (group theory)
Lagrange's theorem, also called Lagrange's Group Theorem, is a result in group theory stating that the order of any subgroup of a finite group divides the order of the group.
Lakh (लाख)
Lakh (लाख), also spelled lac, is a unit in the Indian numbering system equal to one hundred thousand, the standard large-number word in South Asian finance and everyday speech.
Lanczos algorithm
The Lanczos algorithm, also called the Lanczos method, is an iterative method introduced by Cornelius Lanczos in 1950 for finding extreme eigenvalues of large sparse symmetric matrices.
Landau's problems
Landau's problems, or Landau's conjectures, are four unsolved statements about prime numbers, named by Edmund Landau at the 1912 International Congress of Mathematicians in Cambridge as unattackable.
Landweber iteration
Landweber iteration is a gradient-descent method for solving ill-posed linear inverse problems, introduced by Louis Landweber in 1951 and used in image deblurring and tomography.
Langlands dual group
The Langlands dual group of a reductive group G, introduced by Robert Langlands in the late 1960s, is the reductive group obtained by exchanging characters with cocharacters and roots with coroots.
Langlands program
The Langlands program, also known as the Langlands conjectures, is a collection of conjectures proposed by Robert Langlands in 1967 linking Galois representations and automorphic forms.
Langlands–Shahidi method
The Langlands–Shahidi method is a technique in automorphic forms that proves analytic continuation and functional equations for automorphic L-functions by studying constant terms of Eisenstein series.
LAPACK
LAPACK (Linear Algebra Package) is a freely available Fortran library, first released in 1992, for solving linear systems, least-squares, eigenvalue, and singular value problems for dense and banded matrices.
Laplacian matrix
The Laplacian matrix, also called the graph Laplacian or Kirchhoff matrix, is a graph matrix L = D − A whose eigenvalues reveal connectivity, spanning trees, and clustering.
Large cardinal hierarchy
The large cardinal hierarchy orders large-cardinal axioms by consistency strength, usually as a chain of equiconsistencies running from measurable cardinals up to the rank-into-rank axioms, the strongest not known to contradict choice.
Large numbers
Large numbers, or very large numbers, are numbers far beyond everyday counting, conventionally starting around a million, expressed through -illion names, scientific notation, SI prefixes, and googology.
Large sieve
The large sieve is a method in analytic number theory, introduced by Yuri Linnik in 1941, that controls a sequence of numbers simultaneously modulo many small moduli.
Largest known prime number
The largest known prime number, the Mersenne prime 2^136,279,841 − 1, has 41,024,320 digits and was found by Luke Durant via the GIMPS project in 2024.
Lattice (order)
A lattice is a partially ordered set in which every pair of elements has a greatest lower bound (meet) and a least upper bound (join).
Lattice-ordered group
A lattice-ordered group, also called an ℓ-group, is a group with a partial order under which every two elements have a meet and join, preserved by all translations.
Least common multiple
The least common multiple (LCM), also called the smallest common multiple, is the smallest positive integer that two nonzero integers both divide evenly, such as lcm(6, 9) = 18.
Least-upper-bound property
The least-upper-bound property, also called the supremum property, says every nonempty subset of an ordered set that is bounded above has a least upper bound in the set.
Legendre symbol
The Legendre symbol, also called the quadratic residue symbol, is a function from number theory that tells whether an integer is a quadratic residue modulo an odd prime p.
Legendre's conjecture
Legendre's conjecture is an unsolved problem in number theory stating that there is at least one prime between every pair of consecutive squares, proposed by Adrien-Marie Legendre in 1808 and still unproven.
Leibniz formula for determinants
The Leibniz formula for determinants expresses the determinant of an n × n matrix as a signed sum over all n! permutations, a definition introduced by Leibniz in 1693.
Leibniz formula for π
The Leibniz formula for π, also called the Gregory–Leibniz series, is the alternating series 1 − 1/3 + 1/5 − 1/7 + ⋯ that sums to π/4.
Lemniscate
The lemniscate of Bernoulli is a figure-eight plane curve, defined by a constant product of distances from two fixed points, published by Jacob Bernoulli in 1694.
Lenstra–Lenstra–Lovász lattice basis reduction algorithm
The Lenstra–Lenstra–Lovász (LLL) algorithm, introduced by Arjen Lenstra, Hendrik Lenstra, and László Lovász in 1982, transforms any lattice basis into a reduced basis with short, nearly orthogonal vectors in polynomial time.
Leray spectral sequence
The Leray spectral sequence is a spectral sequence, introduced by Jean Leray in 1945 alongside sheaf theory, that computes the cohomology of a space from a continuous map's fibers.
Less-than sign
The less-than sign, or less-than symbol, is the mathematical symbol <, indicating that the value on its left is smaller than the value on its right.
Levent Alpöge
Levent Alpöge is an American–Turkish number theorist known for results on elliptic curves and a negative solution of Hilbert's tenth problem over rings of integers.
Levi-Civita field
The Levi-Civita field is a non-Archimedean ordered field extension of the real numbers containing infinitesimals, the smallest such extension that is real closed and Cauchy complete.