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22 relations: Acta Arithmetica, American Journal of Mathematics, Comptes rendus de l'Académie des Sciences, Dirichlet's approximation theorem, Effective results in number theory, Experimental Mathematics (journal), Explicit formulae (L-function), Georg Kreisel, International Journal of Number Theory, John Edensor Littlewood, Logarithmic integral function, London Mathematical Society, Mathematics of Computation, Natural density, Natural number, Number theory, Prime-counting function, Riemann hypothesis, Riemann zeta function, South Africa, Stanley Skewes, Upper and lower bounds.
Acta Arithmetica
Acta Arithmetica is a scientific journal of mathematics publishing papers on number theory.
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American Journal of Mathematics
The American Journal of Mathematics is a bimonthly mathematics journal published by the Johns Hopkins University Press.
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Comptes rendus de l'Académie des Sciences
Comptes rendus de l'Académie des Sciences (English: Proceedings of the Academy of sciences), or simply Comptes rendus, is a French scientific journal which has been published since 1666.
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Dirichlet's approximation theorem
In number theory, Dirichlet's theorem on Diophantine approximation, also called Dirichlet's approximation theorem, states that for any real number α and any positive integer N, there exists integers p and q such that 1 ≤ q ≤ N and This is a fundamental result in Diophantine approximation, showing that any real number has a sequence of good rational approximations: in fact an immediate consequence is that for a given irrational α, the inequality is satisfied by infinitely many integers p and q. This corollary also shows that the Thue–Siegel–Roth theorem, a result in the other direction, provides essentially the tightest possible bound, in the sense that the bound on rational approximation of algebraic numbers cannot be improved by increasing the exponent beyond 2.
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Effective results in number theory
For historical reasons and in order to have application to the solution of Diophantine equations, results in number theory have been scrutinised more than in other branches of mathematics to see if their content is effectively computable.
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Experimental Mathematics (journal)
Experimental Mathematics is a quarterly scientific journal of mathematics published by A K Peters, Ltd. until 2004, now by Taylor & Francis.
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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.
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Georg Kreisel
Georg Kreisel FRS (September 15, 1923 – March 1, 2015) was an Austrian-born mathematical logician who studied and worked in Great Britain and America.
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International Journal of Number Theory
The International Journal of Number Theory was established in 2005 and is published by World Scientific.
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John Edensor Littlewood
John Edensor Littlewood FRS LLD (9 June 1885 – 6 September 1977) was an English mathematician.
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Logarithmic integral function
In mathematics, the logarithmic integral function or integral logarithm li(x) is a special function.
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London Mathematical Society
The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS) and the Institute of Mathematics and its Applications (IMA)).
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Mathematics of Computation
Mathematics of Computation is a bimonthly mathematics journal focused on computational mathematics.
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Natural density
In number theory, natural density (or asymptotic density or arithmetic density) is one of the possibilities to measure how large a subset of the set of natural numbers is.
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Natural number
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
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Number theory
Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.
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Prime-counting function
In mathematics, the prime-counting function is the function counting the number of prime numbers less than or equal to some real number x. It is denoted by (x) (unrelated to the number pi).
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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.
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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.
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South Africa
South Africa, officially the Republic of South Africa (RSA), is the southernmost country in Africa.
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Stanley Skewes
Stanley Skewes (1899–1988) was a South African mathematician, best known for his discovery of the Skewes's number in 1933.
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Upper and lower bounds
In mathematics, especially in order theory, an upper bound of a subset S of some partially ordered set (K, ≤) is an element of K which is greater than or equal to every element of S. The term lower bound is defined dually as an element of K which is less than or equal to every element of S. A set with an upper bound is said to be bounded from above by that bound, a set with a lower bound is said to be bounded from below by that bound.
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Redirects here:
Skewe's Number, Skewe's number, Skewes number, Skewes' number, Skewes’s number, Π(x) − Li(x).
References
[1] https://en.wikipedia.org/wiki/Skewes's_number
