Faster access than browser!
47 relations: Adele ring, Alain Connes, American Mathematical Society, Analytic number theory, Andrew Odlyzko, Atle Selberg, Atomic nucleus, Canonical coordinates, Carl M. Bender, David Hilbert, Dilation (operator theory), Dirac delta function, Dorje C. Brody, Edmund Landau, Eigenvalues and eigenvectors, Energy level, Expected value, Explicit formulae (L-function), Fredholm integral equation, Freeman Dyson, Functional analysis, Göttingen, George Pólya, Hamiltonian (quantum mechanics), Hermitian matrix, Hugh Lowell Montgomery, Institute for Advanced Study, Jonathan Keating, Laplace operator, Mathematics, Michael Berry (physicist), Montgomery's pair correlation conjecture, Noncommutative geometry, Perturbation theory (quantum mechanics), Quantization (physics), Quantum mechanics, Quantum state, Random matrix, Resolvent formalism, Riemann hypothesis, Riemann surface, Riemann zeta function, Schrödinger equation, Selberg trace formula, Self-adjoint operator, Spectral theory, Spectrum.
Adele ring
In mathematics, the adele ring (also adelic ring or ring of adeles) is defined in class field theory, a branch of algebraic number theory.
New!!: Hilbert–Pólya conjecture and Adele ring · See more »
Alain Connes
Alain Connes (born 1 April 1947) is a French mathematician, currently Professor at the Collège de France, IHÉS, Ohio State University and Vanderbilt University.
New!!: Hilbert–Pólya conjecture and Alain Connes · See more »
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
New!!: Hilbert–Pólya conjecture and American Mathematical Society · See more »
Analytic number theory
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers.
New!!: Hilbert–Pólya conjecture and Analytic number theory · See more »
Andrew Odlyzko
Andrew Michael Odlyzko (born 23 July 1949) is a mathematician and a former head of the University of Minnesota's Digital Technology Center and of the Minnesota Supercomputing Institute.
New!!: Hilbert–Pólya conjecture and Andrew Odlyzko · See more »
Atle Selberg
Atle Selberg (14 June 1917 – 6 August 2007) was a Norwegian mathematician known for his work in analytic number theory, and in the theory of automorphic forms, in particular bringing them into relation with spectral theory.
New!!: Hilbert–Pólya conjecture and Atle Selberg · See more »
Atomic nucleus
The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment.
New!!: Hilbert–Pólya conjecture and Atomic nucleus · See more »
Canonical coordinates
In mathematics and classical mechanics, canonical coordinates are sets of coordinates on phase space which can be used to describe a physical system at any given point in time.
New!!: Hilbert–Pólya conjecture and Canonical coordinates · See more »
Carl M. Bender
Carl M. Bender (born 1943) is an American applied mathematician and mathematical physicist.
New!!: Hilbert–Pólya conjecture and Carl M. Bender · See more »
David Hilbert
David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician.
New!!: Hilbert–Pólya conjecture and David Hilbert · See more »
Dilation (operator theory)
In operator theory, a dilation of an operator T on a Hilbert space H is an operator on a larger Hilbert space K, whose restriction to H composed with the orthogonal projection onto H is T. More formally, let T be a bounded operator on some Hilbert space H, and H be a subspace of a larger Hilbert space H'.
New!!: Hilbert–Pólya conjecture and Dilation (operator theory) · See more »
Dirac delta function
In mathematics, the Dirac delta function (function) is a generalized function or distribution introduced by the physicist Paul Dirac.
New!!: Hilbert–Pólya conjecture and Dirac delta function · See more »
Dorje C. Brody
Dorje C. Brody (born 1970 in Hong Kong) is a British applied mathematician and mathematical physicist.
New!!: Hilbert–Pólya conjecture and Dorje C. Brody · See more »
Edmund Landau
Edmund Georg Hermann Landau (14 February 1877 – 19 February 1938) was a German mathematician who worked in the fields of number theory and complex analysis.
New!!: Hilbert–Pólya conjecture and Edmund Landau · See more »
Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
New!!: Hilbert–Pólya conjecture and Eigenvalues and eigenvectors · See more »
Energy level
A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy.
New!!: Hilbert–Pólya conjecture and Energy level · See more »
Expected value
In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents.
New!!: Hilbert–Pólya conjecture and Expected value · See more »
Explicit formulae (L-function)
In mathematics, the explicit formulae for L-functions are relations between sums over the complex number zeroes of an L-function and sums over prime powers, introduced by for the Riemann zeta function.
New!!: Hilbert–Pólya conjecture and Explicit formulae (L-function) · See more »
Fredholm integral equation
In mathematics, the Fredholm integral equation is an integral equation whose solution gives rise to Fredholm theory, the study of Fredholm kernels and Fredholm operators.
New!!: Hilbert–Pólya conjecture and Fredholm integral equation · See more »
Freeman Dyson
Freeman John Dyson (born 15 December 1923) is an English-born American theoretical physicist and mathematician.
New!!: Hilbert–Pólya conjecture and Freeman Dyson · See more »
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense.
New!!: Hilbert–Pólya conjecture and Functional analysis · See more »
Göttingen
Göttingen (Low German: Chöttingen) is a university city in Lower Saxony, Germany.
New!!: Hilbert–Pólya conjecture and Göttingen · See more »
George Pólya
George Pólya (Pólya György; December 13, 1887 – September 7, 1985) was a Hungarian mathematician.
New!!: Hilbert–Pólya conjecture and George Pólya · See more »
Hamiltonian (quantum mechanics)
In quantum mechanics, a Hamiltonian is an operator corresponding to the total energy of the system in most of the cases.
New!!: Hilbert–Pólya conjecture and Hamiltonian (quantum mechanics) · See more »
Hermitian matrix
In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the -th row and -th column is equal to the complex conjugate of the element in the -th row and -th column, for all indices and: Hermitian matrices can be understood as the complex extension of real symmetric matrices.
New!!: Hilbert–Pólya conjecture and Hermitian matrix · See more »
Hugh Lowell Montgomery
Hugh Lowell Montgomery (born August 26, 1944) is an American mathematician, working in the fields of analytic number theory and mathematical analysis.
New!!: Hilbert–Pólya conjecture and Hugh Lowell Montgomery · See more »
Institute for Advanced Study
The Institute for Advanced Study (IAS) in Princeton, New Jersey, in the United States, is an independent, postdoctoral research center for theoretical research and intellectual inquiry founded in 1930 by American educator Abraham Flexner, together with philanthropists Louis Bamberger and Caroline Bamberger Fuld.
New!!: Hilbert–Pólya conjecture and Institute for Advanced Study · See more »
Jonathan Keating
Jonathan Peter Keating FRS is a British mathematician.
New!!: Hilbert–Pólya conjecture and Jonathan Keating · See more »
Laplace operator
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space.
New!!: Hilbert–Pólya conjecture and Laplace operator · See more »
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
New!!: Hilbert–Pólya conjecture and Mathematics · See more »
Michael Berry (physicist)
Sir Michael Victor Berry, (born 14 March 1941), is a mathematical physicist at the University of Bristol, England.
New!!: Hilbert–Pólya conjecture and Michael Berry (physicist) · See more »
Montgomery's pair correlation conjecture
In mathematics, Montgomery's pair correlation conjecture is a conjecture made by that the pair correlation between pairs of zeros of the Riemann zeta function (normalized to have unit average spacing) is which, as Freeman Dyson pointed out to him, is the same as the pair correlation function of random Hermitian matrices.
New!!: Hilbert–Pólya conjecture and Montgomery's pair correlation conjecture · See more »
Noncommutative geometry
Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions (possibly in some generalized sense).
New!!: Hilbert–Pólya conjecture and Noncommutative geometry · See more »
Perturbation theory (quantum mechanics)
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one.
New!!: Hilbert–Pólya conjecture and Perturbation theory (quantum mechanics) · See more »
Quantization (physics)
In physics, quantization is the process of transition from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics.
New!!: Hilbert–Pólya conjecture and Quantization (physics) · See more »
Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
New!!: Hilbert–Pólya conjecture and Quantum mechanics · See more »
Quantum state
In quantum physics, quantum state refers to the state of an isolated quantum system.
New!!: Hilbert–Pólya conjecture and Quantum state · See more »
Random matrix
In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables.
New!!: Hilbert–Pólya conjecture and Random matrix · See more »
Resolvent formalism
In mathematics, the resolvent formalism is a technique for applying concepts from complex analysis to the study of the spectrum of operators on Banach spaces and more general spaces.
New!!: Hilbert–Pólya conjecture and Resolvent formalism · See more »
Riemann hypothesis
In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part.
New!!: Hilbert–Pólya conjecture and Riemann hypothesis · See more »
Riemann surface
In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.
New!!: Hilbert–Pólya conjecture and Riemann surface · See more »
Riemann zeta function
The Riemann zeta function or Euler–Riemann zeta function,, is a function of a complex variable s that analytically continues the sum of the Dirichlet series which converges when the real part of is greater than 1.
New!!: Hilbert–Pólya conjecture and Riemann zeta function · See more »
Schrödinger equation
In quantum mechanics, the Schrödinger equation is a mathematical equation that describes the changes over time of a physical system in which quantum effects, such as wave–particle duality, are significant.
New!!: Hilbert–Pólya conjecture and Schrödinger equation · See more »
Selberg trace formula
In mathematics, the Selberg trace formula, introduced by, is an expression for the character of the unitary representation of on the space of square-integrable functions, where is a Lie group and a cofinite discrete group.
New!!: Hilbert–Pólya conjecture and Selberg trace formula · See more »
Self-adjoint operator
In mathematics, a self-adjoint operator on a finite-dimensional complex vector space V with inner product \langle\cdot,\cdot\rangle is a linear map A (from V to itself) that is its own adjoint: \langle Av,w\rangle.
New!!: Hilbert–Pólya conjecture and Self-adjoint operator · See more »
Spectral theory
In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces.
New!!: Hilbert–Pólya conjecture and Spectral theory · See more »
Spectrum
A spectrum (plural spectra or spectrums) is a condition that is not limited to a specific set of values but can vary, without steps, across a continuum.
New!!: Hilbert–Pólya conjecture and Spectrum · See more »
Redirects here:
Berry Conjecture, Berry conjecture, Berry-Keating conjecture, Hilbert-Polya conjecture, Hilbert-Pólya conjecture, Hilbert–Polya conjecture, Riemann operator.
References
[1] https://en.wikipedia.org/wiki/Hilbert–Pólya_conjecture
