Provides an asymptotic formula for counting the number of prime ideals of a number field
In algebraic number theory, the prime ideal theorem is the number field generalization of the prime number theorem. It provides an asymptotic formula for counting the number of prime ideals of a number field K, with norm at most X.
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in general, so that the primeidealtheorem is dominated by the ideals of norm a prime number. As Edmund Landau proved in Landau 1903, for norm at most...
ISBN 0-8218-2004-4. Landau's function LandauprimeidealtheoremLandau's problems Landau's symbol (Big O notation) Landau–Kolmogorov inequality Landau–Ramanujan...
than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself...
information about generalizations of the theorem. Landauprimeidealtheorem for a generalization to primeideals in algebraic number fields. Riemann hypothesis...
generalisation of the prime number theorem is the Landauprimeidealtheorem, which describes the asymptotic distribution of the ideals in OK. Various arithmetical...
region are called non-trivial zeros. The classical theorem on zero-free regions (Grönwall, Landau, Titchmarsh) states that there exists an effectively...
Retrieved 2 October 2022. Ingham (1932), Theorem 30, p. 83; Montgomery & Vaughan (2007), p. 430. Ingham (1932), p. 82. Landau, Edmund (1924), "Über die Möbiussche...
factorization theorem indicates that every positive integer greater than 1 can be written in only one way as a product of prime numbers. The prime numbers can...
rings, but Noether found a unique factorization theorem, now called the Lasker–Noether theorem, for the ideals of many rings. Much of Noether's work lay in...
example of an ineffective result was J. E. Littlewood's theorem of 1914, that in the prime number theorem the differences of both ψ(x) and π(x) with their asymptotic...
then to each (positive) prime p which does not ramify in K and to each primeideal P lying over p in K there is a unique element g of Gal(K/Q) satisfying...
Mersenne numbers. Landau's problems Goldbach conjecture: all even natural numbers greater than 2 {\displaystyle 2} are the sum of two prime numbers. Legendre's...
distribution The hyperbolic secant distribution The Johnson SU distribution The Landau distribution The Laplace distribution The Lévy skew alpha-stable distribution...
Hardy's Theorem while the version by Bonami–Demange–Jaming covers the full strength of Hardy's Theorem. A different proof of Beurling's theorem based on...
The fundamental theorem of arithmetic states that any positive integer n can be represented uniquely as a product of powers of primes: n = p 1 a 1 ⋯ p...
observers correspond to a certain Riemannian metric, now called the Langevin-Landau-Lifschitz metric. 1937: Jan Weyssenhoff (now perhaps best known for his...
paramagnetic susceptibility is a macroscopic effect and has to be contrasted with Landau diamagnetic susceptibility which is equal to minus one third of Pauli's...
Pāṇini). 600 BC: Thales of Miletus discovers Thales's theorem. 600 BC: Maharshi Kanada gives the ideal of the smallest units of matter. According to him,...
Contextuality may be traded-off against Landauer erasure to obtain equivalent advantages. The Kochen–Specker theorem proves that quantum mechanics is incompatible...
equation by using the Chinese remainder theorem to piece together solutions modulo powers of each different prime number. Named after Helmut Hasse. Hauser's...
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