Landau-Ramanujan constant
Encyclopedia
In mathematics
, the Landau–Ramanujan constant occurs in a number theory
result stating that the number of positive integers less than x that are the sum of two square number
s, for large x, varies as
The constant
of proportionality is the Landau–Ramanujan constant, which was discovered independently by Edmund Landau
and Srinivasa Ramanujan
.
More formally, if N(x) is the number of positive integers less than x which are the sum of two squares, then
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the Landau–Ramanujan constant occurs in a number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
result stating that the number of positive integers less than x that are the sum of two square number
Square number
In mathematics, a square number, sometimes also called a perfect square, is an integer that is the square of an integer; in other words, it is the product of some integer with itself...
s, for large x, varies as
Proportionality (mathematics)
In mathematics, two variable quantities are proportional if one of them is always the product of the other and a constant quantity, called the coefficient of proportionality or proportionality constant. In other words, are proportional if the ratio \tfrac yx is constant. We also say that one...
The constant
Mathematical constant
A mathematical constant is a special number, usually a real number, that is "significantly interesting in some way". Constants arise in many different areas of mathematics, with constants such as and occurring in such diverse contexts as geometry, number theory and calculus.What it means for a...
of proportionality is the Landau–Ramanujan constant, which was discovered independently by Edmund Landau
Edmund Landau
Edmund Georg Hermann Landau was a German Jewish mathematician who worked in the fields of number theory and complex analysis.-Biography:...
and Srinivasa Ramanujan
Srinivasa Ramanujan
Srīnivāsa Aiyangār Rāmānujan FRS, better known as Srinivasa Iyengar Ramanujan was a Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series and continued fractions...
.
More formally, if N(x) is the number of positive integers less than x which are the sum of two squares, then