In mathematics, Hardy's theorem is a result in complex analysis describing the behavior of holomorphic functions. Let f {\displaystyle f} be a holomorphic...

Hardy–Ramanujan Journal Hardy–Ramanujan number Hardy–Ramanujan theorem Hardy's inequality Hardy's theorem Hardy field Hardy Z function Pisot–Vijayaraghavan number...

In mathematics, the Hardy–Ramanujan theorem, proved by Ramanujan and checked by Hardy states that the normal order of the number ω ( n ) {\displaystyle...

Hardy's theorem (complex analysis) Hartogs–Rosenthal theorem (complex analysis) Harnack's theorem (complex analysis) Hurwitz's automorphisms theorem (algebraic...

In mathematical analysis, the Hardy–Littlewood Tauberian theorem is a Tauberian theorem relating the asymptotics of the partial sums of a series with...

principle Logarithmically convex function Hardy's theorem Hadamard three-line theorem Borel–Carathéodory theorem Phragmén–Lindelöf principle Ullrich 2008...

In population genetics, the Hardy–Weinberg principle, also known as the Hardy–Weinberg equilibrium, model, theorem, or law, states that allele and genotype...

in 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...

In probability theory and statistics, Campbell's theorem or the Campbell–Hardy theorem is either a particular equation or set of results relating to the...

in some sense. (For related results, see Prime number theorem § Prime number race.) In 1923, Hardy and Littlewood showed that the generalized Riemann hypothesis...

In number theory, Euler's theorem (also known as the Fermat–Euler theorem or Euler's totient theorem) states that, if n and a are coprime positive integers...

almost everywhere for functions in L 1 {\displaystyle L^{1}} . This theorem of G. H. Hardy and J. E. Littlewood states that M is bounded as a sublinear operator...

Borel–Carathéodory theorem Corona theorem Hadamard three-circle theorem Hardy space Hardy's theorem Maximum modulus principle Nevanlinna theory Paley–Wiener theorem Progressive...

prove the Sobolev embedding theorem, giving inclusions between certain Sobolev spaces, and the Rellich–Kondrachov theorem showing that under slightly...

mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer...

conjecture, the Hardy–Littlewood conjecture (see below), postulates a distribution law for twin primes akin to the prime number theorem. On 17 April 2013...

Hardy's inequality is an inequality in mathematics, named after G. H. Hardy. Its discrete version states that if a 1 , a 2 , a 3 , … {\displaystyle a_{1}...

he sent Hardy a letter packed with theorems, writing, "I have found a friend in you who views my labour sympathetically." To supplement Hardy's endorsement...

fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus...

In mathematics, Abelian and Tauberian theorems are theorems giving conditions for two methods of summing divergent series to give the same result, named...

commonly written as ln(x) or loge(x). In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among...

Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with...

a given magnitude by generalizing the prime number theorem. It was first proposed by G. H. Hardy and John Edensor Littlewood in 1923. Let m 1 , m 2 ...

In mathematical logic, Goodstein's theorem is a statement about the natural numbers, proved by Reuben Goodstein in 1944, which states that every Goodstein...

In number theory, Vinogradov's theorem is a result which implies that any sufficiently large odd integer can be written as a sum of three prime numbers...

Beurling–Lax theorem is a theorem due to Beurling (1948) and Lax (1959) which characterizes the shift-invariant subspaces of the Hardy space H 2 ( D...

In mathematics, a Paley–Wiener theorem is a theorem that relates decay properties of a function or distribution at infinity with analyticity of its Fourier...

Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers. It was first proven by Euclid...

essay by British mathematician G. H. Hardy which defends the pursuit of mathematics for its own sake. Central to Hardy's "apology" – in the sense of a formal...

(1976), p. 296. Hardy & Wright (2008), pp. 342–347, §18.1. Apostol (1976), Theorem 3.3. Hardy & Wright (2008), pp. 347–350, §18.2. Hardy & Wright (2008)...