L-notation is an asymptotic notation analogous to big-O notation, denoted as ${\displaystyle L_{n}[\alpha ,c]}$ for a bound variable ${\displaystyle n}$ tending to infinity. Like big-O notation, it is usually used to roughly convey the rate of growth of a function, such as the computational complexity of a particular algorithm.

It is defined as

where c is a positive constant, and ${\displaystyle \alpha }$ is a constant ${\displaystyle 0\leq \alpha \leq 1}$.

L-notation is used mostly in computational number theory, to express the complexity of algorithms for difficult number theory problems, e.g. sieves for integer factorization and methods for solving discrete logarithms. The benefit of this notation is that it simplifies the analysis of these algorithms. The ${\displaystyle e^{c(\ln n)^{\alpha }(\ln \ln n)^{1-\alpha }}}$ expresses the dominant term, and the ${\displaystyle e^{o(1)(\ln n)^{\alpha }(\ln \ln n)^{1-\alpha }}}$ takes care of everything smaller.

When ${\displaystyle \alpha }$ is 0, then

is a polylogarithmic function (a polynomial function of ln n);

When ${\displaystyle \alpha }$ is 1 then

is a fully exponential function of ln n (and thereby polynomial in n).